" bought a used set of Pings for my irons. Driver is a Taylor Made. Gap wedges are Clevelands. "

You have good clubs, the lie angle and shafts would be the next question. Just because they are good clubs doesn't mean they are the best for you, but probably not holding you back much at bogey golf.

If you play 3-4 times per week; hit, chip, and putt on the off days; take a lesson every 2-3 weeks; and get the right set of clubs... in 1.5 - 2 years you will be as good as you are going to get.
You will win tons of money while the handicap is dropping. After that you, as noted by Uncle Alps, most look for ways to keep it a little higher.
Athleticism is one factor, hand eye (not the same) is another, so is mental compatibility with the game. Just about everyone can get to 10-15 without much problem, once one gets to 0-5 or lower...it is all about what you were born with and how much effort you put in.

my $.02