Had mine for 20 years with nothing major yet(knock on wood). Just changed seals in steering cylinder last week. It has spent most of it's time bush hogging or loader work. Used for hay this summer and it did quite well. I need mfwd so there is a 5095m in the future but I'll keep the 5300. We have done a lot of work together and I just couldn't ler her go.
Most common problem on those unit is operators putting the machine in park, before they're fully stopped. This results in a broken park pawl. Cheap part, expensive to replace. Otherwise very reliable.
The 5210 and 5300 are very similar and in the year and half I put 160 hours on my tractor, I have been very happy with mine. I second Kjung17 comment and if the tractor has MFWD it can affect that as well and get really expensive. If you decide to make the purchase, consider posting that and I will post some URL痴 I have found on my 5210 on the John Deere web-site, which apply to the 5300 as well. My biggest concern no matter what tractor it is would be how well has it been maintained, the number of hours and how it has been used.