On one of my SCCM 2012 R2 clients, the client uninstalls and reinstalls itself every 5 hours.

It sounds like there's a "Install client" stuck somewhere with the "uninstall first" option chosen.   I'm open to ideas to troubleshoot and hunt this sucker down.

The client agent won't uninstall itself. There must be something else involved like possibly the ccmeval task.

Have you reviewed ccmsetup.log and the other logs in ccmsetup\logs?

I've seen the install loop when someone tries to manually install a client, but does it many times.  It just keeps looping.  That's not the case for you because it is waiting 5 hours.

I think your install is failing along the way.  Check the CCMSETUP and CCMEVAL log that Jason suggested, and post a snip here if you have any questions. 

I noticed in my ccmsetup.log that it was trying to install, and felt it needed to UNINSTALL before installing, so I have actually uninstalled (ccmsetup /uninstall) and then manually installed.  I am monitoring now to see if it has broken its cycle.