Yes Howard I know 5/8 is thickness.

At the Home Depot near me floor underlay boards are available in 4 by 4 size only. Sort of half sheet squares.
If it is in 4/8 sheets and you feel it is smooth enough for a paint finish you can probably make do with it. You will probably have to primer and paint as the surface will absorb paint more then MDF.
If you are looking for a
really smooth finish then go MDF
The Melamine sheets are particle board coated with a melamine veneer.
In your first post you didnt say that your could get 3/4 MDF just that your could not get 5/8. Go with the 3/4 MDF and you will not have to worry about finnish problems.
BobA