Sale of primary home - lived and owned only 2 years - do I have to pay capital gains since I didn't owned the house for 5 years?

You don't have to have owned the home for 5 years. To get the exclusion, you have to have owned and lived in the home for 2 out of the last 5 years ending on the date of sale.

Also note that 2 years is not an estimate.  It is exactly 2 years or more from date of purchase.

See OP's other post:
<a rel="nofollow" target="_blank" href="https://ttlc.intuit.com/questions/3403562-seller-closing-date-and-tax-liability">https://ttlc.intuit.com/questions/3403562-seller-closing-date-and-tax-liability</a>