http://www.nolo.com/legal-encyclopedia/free-books/renters-rights-book/chapter3-4.html
Research if VA has a grace period. My guess is that it does not. Your tenant might just have invented something up.
If you determines the VA law does not have such rule, then your contract controls. Read the contract literally: if landloard don't receive payment in 5 days, landlord will charge late fee. Postmark has nothing to with anything.