The older one (radeon) is the one you should have. There are 2 of those and the newer one (AMDGPU) is only for newer cards than yours. So you'er stuck with the open source driver.
AMD FIREPRO V4800 DRIVERS DRIVERS
There are no AMD proprietary binary video drivers for mint 18/ubuntu 16.04 as of this time and AFAIK there's no firm date for when they will be released. Your AMD card is based on the HD 5670 chipset. To show more useful info copy/paste this intpo terminal and copy/paste the text output here: it may seem obvious to a WIndows user to do that but the versions on mfr's sites usually won't work. But I hope it wasn't drivers you dl'ed from the AMD site. Which AMD drivers? Your post isn't very clear. I know the AMD/ATI drivers are still installed. I'm totally overwhelmed by all the dead ends google has led me to with this. I gather there are diagnostic tools but not sure where to start. Now the DVDROM won't even make the display come on, need whatever the second choice is on that first menu. Oh yeah, I have re-installed the OS three times today.
AMD FIREPRO V4800 DRIVERS HOW TO
I have no earthly idea where to look or how to track down what is going on. But decided to try Linux as a replacement for office stuff, and Mint was recommended. I'm not new to Linux, but the past 22 years with it has mainly been spent with Slackware in a non gui environment. But so is Vesa, but it seems that the Vesa driver isn't working since the resolution is limited. Now I know the AMD/ATI drivers are still installed. The boards were chosen when I had lots of windows issues with NVidia. I have another of the same computer in my office, same display board. It boot up to Mint, warning about the display driver not working and resolution is lower than it had been. Then in grub I edited the kernel commands to include nomodeset.
So I killed power as ctl-alt-del didn't work. Just froze that way, blank display, fans making noise.
I had not boot to Mint for a few weeks, but this weekend I had a need to get it in Linux and when I reboot I got blank screen, and the power supply fans and CPU fans all kicked into high gear, the PC never boot up. the machine is a Dell Precision T7500 dual Xeons, 48GB ram, dual 1TB RAID arrays, one for Linux, one for Windows. It worked, it was a simple fix, and fine, got resolution to 1920X1080, using vesa. What I found back then was a post suggesting to force vesa, so I did that xforcevesa (or maybe it was nomodeset) in grub. I struggled in late October for several days to get the display to work.