I am a permanent resident in USA for last 5 years. I sold my home in India in May end this year, and purchasing a home in USA by October end for much larger amount. Do I get any relief in INDIA from capital gain tax?

Cannot say; no expertse on India taxes.

However, you MUST claim that capital gain on your U.S. tax return. If you also must pay capital gains tax to India, you will be able to claim a credit for that tax p[aid using Form 1116.