Will i5 RAM work on an i3 CPU

RAM isnt made for a specific CPU, the kits that say they are for i5's and i7's are listed as such because the new intel CPU memory controllers burn out at over 1.65V, previously there had been kits that ran at 1.9V which is safe for the memory, and for AMD memory controllers but not for Intel ones. Memory listed as being for i5's and i7's will work perfectly fine with an i3.

Thanks very much for the info. In follow up.. I was getting a blue screen but now that I have adjusted the bios from Turbo to standard speed and so far I have not gotten a blue screen. Do you think the turbo setting may be an issue for my configuration?

Did you set the memory speed, timings, and voltage on your memory manually? That is more likely to be a cause of an issue than Turbo boost. When you were blue screening do you happen to remember what the error code was, this article may be able to help you pinpoint your issue.
http://www.maximumpc.com/article/features/blue_screen_s...

It could be as turbo or any other BIOS performance enhance setting may cause instability of the system. Some computer parts just cannot follow the dynamic performance fluctuations and fail causing a BSOD. I usually keep all these auto performace settings off to avoid such situations.

The blue screen was very fast and hard to read, but I could tell that it was memory issue and it said Local ID:1033 BCCode: 24

Yes, it is most likely the Turbo mode. I've tried that with my old setup, and it turns out to be unstable. Take socratesx's advice to avoid automated settings like that.

When you config the BIOS set it first to default and watch what will happen.