The Nikon F5 represents the pinnacle of professional 35mm film bodies, and is the natural extension of the line of 35mm pro bodies that started with the Nikon F almost 50 years ago.   While Nikon has introduced a successor to the F5 in the F6, it is not really a true professional camera body as defined by Nikon and represents an extension of the prosumer cameras such as the N90 and F100.

Nikon professional bodies have a number of features that separate them from other Nikon products:

1. Interchangible viewfinder system, including prism, waist-level and special purpose viewfinders.
2. High speed motor drives.    The F5 was able to integrate the motor drive system into the camera body because of advances in motor technology.   Early cameras like the F,F2 and F3 had very large motors that were detachable.   In any case, the F-series cameras always had the highest frame rates available in the Nikon lineup.
3. Rugged, high quality chassis and shutter.    These professional products are made to shoot many thousands of rolls of films with high levels of reliability, often with very large and heavy lenses mounted, and the chassis and shutter mechanisms are the consistently the best Nikon offers.  F-series cameras also have dust and moisture seals to allow the cameras to be used in inclement conditions. 
4. Full System of Components and Lenses.   Again, for professional use, the F-series cameras included a full range of gadgets and attachments to maximize the utility of the camera for professional use.
5. Minimal automation and maximum safety interlocks for use under difficult conditions.   Another mark of the F-series cameras are interlocks and a lack of amateur crutches like "picture" modes.

While the F5 shares these pro features, many are missing from the F6, hence my assertion that the F-series line of pro camera bodies ends at the F5.     Nikon diluted the F series with the introduction of the F100, which was nothing more than a continuation of the "prosumer"  N90.    The F moniker was attached to appeal to amateur photographers and give the F100 the shine of a pro camera, but the F100 never had any of the main features of the F series.   In other words, the F100 was a marketing ploy.  (And excellent camera, nonetheless.)    Because the film SLR has become a dead product for most professional photographers, Nikon declined to invest in a worthy successor to the F5, and the updated F100 as F6 was the result.

When shopping for a used F5, remember that this is a camera aimed squarely at professional photographers, and you want to avoid cameras with heavy use.    As rugged as the F5 is, it's easy to get a worn-out unit that was used by a news pool, so be patient and look for a camera that doesn't have a lot of obvious wear on the body.

Here's an inspection check list:

1. Battery box and battery.   Make sure the battery tray fits well and the latches work.   The F5 as a number of battery options.  The basic camera includes a tray to hold AA batteries and this should always be included.    Rechargible batteries must include the charger and the battery should be able to hold a normal charge.   They are expensive to replace and you should make sure the seller guarantees the rechargible battery.  If not, bid lower.
2. Viewfinder system.   Release the viewfinder by pushing the release button the the back of the finder and pulling the viewfinder backwards.   Avoid a camera with a dented finder cover-- this is a magnesium part and is very strong, and such a camera has been dropped.  Don't buy it.   Make sure the seals are intact, the viewfinder shutter works and the control switches work.   The viewfinder should not have any dust or moisture inside-  If so, the seals are damaged and you should avoid the camera.    Check the focus screen.   The F5 focus screen is an active component and a well-known problem is separation of the screen, which will show up as fuzzy or iridescent patches.    This will need to be replaced at a cost of $100 or more, so bid accordingly.    Also, make sure the focus points work on the screen.   Also check the internal viewfinder displays and make sure they are working.   This is a much more expensive repair and you want to avoid a camera with bad viewfinder displays.  The F5 also has a shutter to block the eyepiece and make sure it is working.
3. Body LCD's.    Make sure there is no bleeding of the LCD's and the backlights work.
4. Lens mount and mirror box.   A regular size lens, when mounted, should never wobble on the mount.   The mount ring should be perfectly flat and firmly attached to the body.  The mirror should be clean and not scratched.   The mirror is delicate and not cheap to replace, and mirrors should never be touched with the fingers.   
5. Body controls.    All the body controls should be firm and precise, and many of the controls have interlocks that must be activated to change the control.    Body controls that do not activate a function consistently, indicate heavy wear or failure of the weather seal, and such a camera should be avoided.
6. Motor drive.   Check the motor at different speeds.    When checking the motor, set the camera to manual mode and set the shutter speed to 1/1000 or higher.    Set the aperture control to full open.   Setting too low a shutter speed will cause the motor drive to slow below the set speed.
7. Exposure system.   Use a gray card and a hand-held light meter (if you have one) to check the exposure system modes.     If you mount the camera on a tripod and fix the gray card under uniform lighting so it fills the viewfinder, there should be no change in indicated exposure as you change different modes.   Make sure bracketing and exposure compensation works too.   Remember that exposure readings can be altered by stray light entering the eyepiece, so close the eyepiece shutter and watch the top LCD when you check the exposure system.
8. Flash system.   The flash metering system is independent of the ambient light metering system and if you can, take a compatible speedlight like the SB28 to check the flash system.     Without film, you'll be looking for flash output that changes with different subjects, and believable response from the flash system over and under exposure signals in the viewfinder, as well as proper coupling of the camera body to the flash system.   The Nikon D-flash system reports focus points to the flash when used with D-series lenses, and the distance scales on a compatible flash should change as you change exposure settings.
9. Body integrity.    The F5 has a very rugged body and any dents, cracks or splits are evidence that the camera has been dropped and/or abused.  Avoid such cameras.  There are plenty of clean used F5's on the market so there is no need to buy a worn out body.     One common problem with the F5 is the rubber covering delaminating, and this can be repaired with contact cement.    This seems to be a random problem rather than an indicator of abuse, so look for other problems like dents and paint wear if the camera coating is loose.   Check the tripod socket and bottom of the camera to make sure it is in good condition.    Wear on the bottom of the camera is normal even with cameras that are not heavily used.
10. Film compartment.    A worn pressure plate, bent back cover or damage hinges, and wear of the film guides and take up is a sure sign of a camera to be avoided.

A final test for every camera is the test roll of film.  I always used slide film for this test because it eliminates the variables of the printing process.   If you can, include test cards like the Macbeth color checker and also compare the camera's exposure system to that of a hand-held meter, especially an incident meter if you have access to one.  You can also include some focus accuracy tests and a backfocus test if you have a number of lenses.   Any F5 seller should allow a test roll to be shot-- It's the photographic equivalent of test driving a car.   A seller who refuses such a test and insists on "as-is" selling with no return should be avoided, or you should bid accordingly.   I would not bid more than a few hundred dollars on such a camera, no matter how good it looks.   If the seller has a lot of neutrals and negatives for misprepresentation, take that as an addition warning sign not to buy as-is items from them.

That's a lot to check but the F5 is a lot of camera.     In amateur hands, a clean F5 will easily outlast the owner's ability to buy and process film.    My three F5's were used professionally for over a decade and exposed thousands of rolls of film, but worked perfectly and were in good cosmetic condition when I replaced them with digital cameras.    If you take the time to look for such a camera, you'll get what was the ultimate expression of Nikon's professional SLR cameras.   If it's too big and heavy, look to "prosumer" cameras like the N90s and F100, but if you want the best of Nikon, go for the F5.