Will I pay investment taxes when selling my 1st home? Purchased May 2018, close on new home Apr2020, but will live in 1st home until May 5, 2020 before moving to new home

If the 1st home is your primary residence for 24 of the previous 60 months at the time you sell it, it will qualify for the tax exemption.  The amount of gain exempted is $500,000 if married filing joint, or $250,000 if single.  

To qualify for the exclusion of the capital gain, on the sale off your primary home, you must both OWN the home and live in the home for 2 out of the 5 years prior to the sale.  May 2018 to April 2020 comes up short on the ownership requirement.

Postpone closing until after you meet the full 2 years. Also be careful on the live in time. 2 years is 731 days.