7 Day JR Pass or 5 Day JR Pass?

I am travelling from Tokyo to Kyoto, then stay 3 nights in Kyoto. In my 3 nights' stay in Kyoto, I will explore Kyoto, Nara, Himeji and maybe Osaka on day trips. After that I will return to Tokyo, explore and stay another 4 nights in Tokyo. Which JR Pass should I buy? The 7 Day JR Pass or the 5 Day JR Pass? Is it true that in Tokyo, it is cheaper and more convenient to use the Metro as compared to the Rail? Thank you.

Which JR Pass should I buy? The 7 Day JR Pass or the 5 Day JR Pass?

There is no 5 day pass! See here:
http://www.japan-guide.com/e/e2361.html

Is it true that in Tokyo, it is cheaper and more convenient to use the Metro as compared to the Rail?

Not, it is not true (assuming you mean JR when refering to "Rail"). As for convenience, it depends on from where to where you want to get. Sometimes, a combination of subway and JR is most convenient. As for price, subways and JR are about equally cheap. JR is somewhat cheaper on short distances, while subways are somewhat cheaper on longer distances.

Thank you for your help. I really appreciate it very much.

Is it true that in Tokyo, it is cheaper and more convenient to use the Metro as compared to the Rail?
If you get a rail pass, the JR trains are for free and that is difficult to beat, price-wize. Of the touristy areas in Tokyo, I think it is only Roppongi and Asakusa that require you to use the subway, otherwise there is always a JR station nearby. Note that for Asakusa you might need to change subway companies, so you'll need to pay again. I believe that there is a subway pass that works regardless of what company you use.

Of the touristy areas in Tokyo, I think it is only Roppongi and Asakusa that require you to use the subway,

Odaiba is also accessible by non-JR transportation only.