Personally, I wouldn't want to run it at 80 under normal load..
Can it handle it? Yes it does, but this will make it degrade over time since it's in risk of going higher under load...
I have few suggestions for you, I can explain them step by step but this would take time, so feel free to make your researches based on my suggestions, and add Additional details if you needed some more details about something specific..
Cooling:
- If you're low on budget, get an aftermarket cheap/efficient cooler such as Hyper212.
- If you're good in budget, you can get a closed loop liquid cooling solution, such as Corsair ( H70 / H80 / and so on )
Underclocking:
Disable the boost in your CPU, running it at 3.3 instead of 3.7 would really matter in temperatures..
Manual Overclocking:
Usually, 'Overclocking' sucks more Voltage than Manual, sometimes way too much that you get high temperatures while you're actually able to run it even at faster clocks with lower temps..
People tend to overclock an i5-2500k to 4.0ghz on Air and still stay safe..
I suggest that you use CPU-Z software, then run Prime95 blend test for few minutes, just to get your CPU under 100% load and read the "Core Voltage" in your CPU-Z Screen, this should give you an idea on how much voltage it's sucking out of your rig.. The higher the voltage, the higher the temperatures will go, and from there you can start lowering your voltage until the safe point..
There's much to explain about this point, do your research and you should be good to go..
- Edit:
Forgot to mention that I personally ran i5-2500k on 4.7Ghz 24/7 so I have had enough experience with it.