Does the run score or is it a timming play?

[first2third]

Bases loaded two outs 3-2 count on the batter, runners are off with the pitch, batter receives ball four. Runner on second base going on the pitch overruns third and the F2 throws to F5 and F5 tags the runner out before they get back to third. The runner who was on third at the time of the pitch does not cross home plate before the out was recorded on the trailing runner at third. I know that the runner at third can advance without liablilty to be put out, but should the run score even though the third out was recorded before they touched home? I felt this was a timming play and said the run did not count, but on an awarded base I am not sure??? Help so I don't mess this up again!