I used to own the 8320, basically the same CPU with a lower base clock speed. 30ºC is fine when idle, nothing to worry about there. I'm not sure how hot these processors can get before they begin to have a negative effect on performance, but personally when I had my 8320 and a 212 EVO I never hit 80 in anything as far as I was aware according to what my temperature reading software was telling me. To be on the safe side lets assume 80ºC is a tad too high.
I've read on forums that some of the FX chip boards don't have reliable temperature sensors, so it could just be an incorrect reading, however there are some things I'd suggest you do to see if it solves the issue:
1: First thing to do would be to make sure you have the front fans in taking air, this probably sounds like a simple step and if you never did anything with the fans they'd have been set-up as intake by default on the front, and exhaust at the back, this is how you want the airflow to be, or at least what has always worked for me (some people may argue otherwise).
2: Remove some of the movements on the top of the case and take readings. Once again, another step you may have already tried, but if not, just see if it makes much of a change,
3: If you bought the processor second-hand it's possible that it was over clocked, if this is the case it would explain the high temperatures as the last person to use it may have been water cooling, if it's a new chip however this will not be the case.
4: It's likely that the cooler is not making proper contact with the surface of the CPU. I'd suggest taking off the CPU cooler, removing the thermal paste from the processor and from the bottom on the heat sink (you can buy cheap kits of solution that correctly removes thermal paste on Amazon), also take the processor out and making sure no paste is underneath it. Carefully reseat the CPU and then apply a small amount of thermal paste to the centre of it (look at a video from LinusTechTips too see just how much you should be applying), and then place the cooler on top of the CPU vertically (This is just my preference as it pulls less heat off the GPU, thus keeping the CPU cooler) and make sure the fan is in taking the cool air that is coming in from the front fans of the case. Next carefully tighten the CPU cooler down and make sure it's tight enough that it's making contact, but not too tight to the point where it could damage the CPU.
Boot the system and monitor the temps in different games/benchmarks. If it's still too hot then it could just be a bad chip, if it's still under warranty try get it replaced and this should solve everything. Adding extra exhaust fans at the top of the case and extra intakes may also help a bit too.
The Define R5 doesn't have the best airflow really as it's quite closed off, I personally had one for a week or two before I resorted back to my full tower, and the whole time I did have it I noticed my temps being about 10 degrees higher than my temps in my full tower, taking the moduvents off helped a bit though. It's not a bad case though, and it really shouldn't be the main factor