I sold my house in 2010 and I lost $20000 (purchase price: $100k; sale price: $80k). It was my primary residential house. I did not know that I can claim capital loss for it. Can I start to claim a capital loss on my 2015 tax return?
Assuming you are in the US, the answer is "no". Loss on a primary residence is not a deduction.
On a side note, returns can only be amended up to 3 years after original filing due date. So whatever the contents of your 2010 tax return, due 4/15/11, April of 2014 was the last chance you'd have had to make any corrections.