What was St Paul's age at the time of his conversion and what was his age when he died? I think that there are no direct answers for this.
I would like to know the age of the Apostle St Paul when he encountered Jesus on the road to Damascus and how long he lived after that.
It is somewhat impossible to know for sure how old St Paul was at the time of his conversion and death.

The Apostle Paul according to Wikipedia was born between the years of 5 BC and 5 AD. Most websites place his birth between the years 3-5 AD.

As for the Apostle's conversion, it seems to have occurred between the years 33-36 AD. Most websites favor the year 33 AD.

And finally, St Paul died as a martyr between the years 62-67 AD.

Thus St Paul was around 30 years of age at the moment of his conversion and 60 years of age at his death.

Sources:

Paul the Apostle (Wikipedia)

How old was the apostle Paul when he died?

Saint Paul the Apostle (Catholic Saints Info.)

St. Paul (Catholic Online)