Sir,
I am also a landlord with home in VA. I live out of town but yesterday a neighbor told my tenant had a uhaul outside and loading furniture.

I had called police to go by to see if property was abandon. I was told police said tenant was in process of moving. I will contact records to see if police report was filed...

I was trying to negotiate an early termination of lease agreement for the 24th. She hasn't paid me for this month rent due on 1st late on the 5th..

Should I serve abandonment notice 5 day notice to pay or quit or just start court process??

First its not a good idea to piggyback your question on another thread. This can lead to confusion. So I've moved your question to its own thread.

I would do the 5 day pay or quit. It would seem she will choose the quit. Include in the notice that she needs to inform you of the decision to move.

You will have her deposit to cover the June rental, unless they leave damages. While she would still owe July since she did not give sufficient notice. It might not be worht pursuing.