I recently installed a radeon HD 5770 into my new desktop and I noticed while its tempurature for say browsing the web is only 50C, when I am playing Red Faction guerilla my GPU temp is around 70C and when playing farcry 2 with Direct X 10 on very high the temp is almost 80C, is that a safe running temp or is that a sign I need to upgrade my GPU or get cooling paste.
Yes, your temps are a bit high.
I have a vapor-x 5770. It idles at 43c and peaks at 70c with gpu fan set on auto (32-43% rpm).
With the fan set to 52% (the highest i can go without it bothering me), it idles at 43c and peaks at 66c.
For less pretentious games (like FIFA), I downclock the card to gpu600/mem800MHz and leave the fan on auto (32-37%)- this way it idles at 42c and peaks at 60c, with average in-game temps around 46c (near idle)- that's on max res and max details.
So if tou don't need all the power, try downclocking. Of course, good airflow helps (i have an Antec P193 with all coolers installed, but I kept under 1400rpm and watercooled cpu).
Install Afterburner and set a manual fan-curve. Most of the graphics cards come with a 40% fan speed until 70-75C and then start to speed up. Set it with 10 levels of difference between fan speed - C and you will be fine. 40% - 50C, 45% - 55C, 50% - 60C and so on.