Please help 2500k peaks at 80C

Hey, I just got a new CPU core i5 2500. It idles at 30-35C. When I play games, Crysis2. I see it stay around 60sC, I alt tab randomly every now and then to check CPU temps and always catch it at that temp.

But when I look at max temp I see it reach the mid 70s once saw 79C as max temp, but never seem to catch it running at that temp when I alt tab.

If I run Prime95, it gets to high 70s in 2-3 minutes, then I close it, so i suspect it would probably go higher. I'm using stock cooler, not overclocked, everything is stock. I tried reseating the heatsink, made sure all the pins are in and stable.

My case temperature is cool, if I over my hand over the CPU fan It doesn't feel particularly hot. But I noticed that one side of the heatsink kind of moves a tinnnnnyyyy bit when I press on it compared to the other side that just doesn't move at all.

So I was wondering, is it possible that the heatsink is crooked or something, that it just doesn't lay completely flat on the cpu.

I don't really intend on overclocking it and I have already invested enough in this new rig, and I had faulty, GPU and PSU! So I just want everything to work  

So what heat sink would you recommend for an 2500k. Not too expensive, a limit of 50$ MAX, I don't want to have to worry about temperatures ever again lol

THANK YOU