I was thinking to grab the data either from Yahoo finance or Google finance. If I remember right, it allows me to get data from past 5 years only. Do you have recommendation for any other resource?

Yahoo and Google are your best bets for historical prices. Just use the adjusted closing price (not the open or unadjusted prices).

Also, what you call a key area is referred to as a "sector" in investing. There are many ETF managers that try to track the various sectors, though your easiest bet might be the Sector SPDRs. Their webpage already has a correlation tool if you just want to use theirs:

http://www.sectorspdr.com/correlation/

Simply enter one of their ETFs (eg. "XLF") and look at the correlation of the other Sector SPDRs.

Thank you for the link. From your experience did you notice any immediate correlation between the sectors or any time delay? If there is some time delay, it might be a key feature to notice for short term trading, sounds right?

Um, what you're referring to is a form of high-frequency trading. For that you'll need (1) a direct connection to the exchange, and possibly even co-location; (2) historical tick data for backtesting; and (3) the hardware and software capable of executing the logic. The kinds of time-sensitive arbitrage opportunities you're hinting at take a TON of skill and start-up capital to perform.

Basically, if you haven't done this kind of stuff before, this not the type of strategy you should start with.