Should I highlight one of my old papers in my last 5 years research achievements, if the old paper got printed recently?
Unless the instructions say otherwise, the "last five years" means the publication date that is written on the published paper is in the past five years.  It does not matter at all how long the paper was under review or in press.

A selection committee may see when the paper is submitted if that information is written on the paper, but they will not need that information.

Submission and revision dates are used when two papers come out from different authors which say the same thing.  Then the dates can indicate who is first.  I wouldn't worry too much about being first, though.