i5-3570 slight overheating

[Codrat]

I've recently bought a new PC. I picked Intel i5-3570 for CPU, as I do not wish to overclock anytime soon. Still, after installing it (with nothing but the stock cooler's thermal paste) I was peaking 85-90C with prime95 and 80-85 while running games on ultra high. I thought that was way too much so I got myself Arctic Silver 5 and the cleaning kit. I cleaned up both the stock cooler and the CPU and applied AS5 using the vertical line method, as suggested on their website.
So far, using prime95 I stay around 80C, and while playing new-ish games it's more like 70-75C. It's a nice improvement, but I still think it's too much.

Is it normal to get such high temperatures on a non-overclocked CPU? I am running it in turbo mode (3.8GHz instead of 3.4), but it still seems too much.
Should I get a new CPU cooler? I've heard alot of good things about Hyper 212 Evo. If I purchase and install that, would my peak temperature drop at least 10 degrees?
Also, I've read AS5 needs 200 hours to settle in. After 200 hours, will there will be a noticeable temperature difference?

I'm pretty stressed about this because my old rig never went past 55-60C no matter what I ran (prime95 included). I'd like to get that going for my new rig too.

Thanks!

P.S. I've got a front 120mm case fan(air flows in), a back 80mm case fan(air flows out) and a 120mm top case fan (air flows out).

 

[jinayhvora]

what's ur ambient temperature? my CPU touches more or less the same temperatures with the stock heatsink without turbo, so i guess its not much of a problem

 

[Codrat]

Well I run my AC at 25C for several hours during the day. So I'd say room temp should be 25-28C.

In idle state, CPU core temps are 35-40C.