A downloadable Honda TRX 500 repair manual is an online aftermarket do-it-yourself repair booklet that is geared more toward backyard mechanics or non-repairman whereas a complimentary factory service manual is an instructional book provided by manufactures and cover every aspect of maintenance, service and repair of their products. 

If you are unfamiliar repairing machinery or working with parts then you should hire a qualified technician when performing complex repairs. If you insist on fixing the 4-wheeler yourself then you should consider acquiring both a repair manual and a factory service manual. 

The reason you should get both: An aftermarket repair manual generally does not contain detailed factory specifications but they do have quality pictures and step-by-step repair instructions that are easy to understand. 

The factory service manual often contains highly detailed diagrams, illustrations, exploded part views but the directions are typically highly intellectual and are worded for persons who have a lot of understanding of mechanical and electrical concepts. Here are links to both a 3rd party repair manual and a factory service manual. 

For reference, one version on the manuals is free of charge and the other is not but I’d recommend getting both if you plan to take apart your ATV in order to examine parts and repair them if necessary.