Dark Ages V1 any% - 5:15.11
Dark Ages: Volume 1 - Prince of Destiny, freeware version; DOSBox version 0.74 at 3000 cycles. The purpose of 3000 cycles is that it's the "default" for DOSBox and it works well for this game, which makes for an entertaining and accessible run.
Start frame is the first appearance of the player character; end frame is when he touches the pedestal just before the end-game screen is played. Note that this is played on easy difficulty, which reduces the number of coins necessary to gain extra life: difficulty can be accessed from the "Game Config" screen on the main menu.
Look what I found in my computer's back pocket! Dark Ages is a game I have a very weird memory of, because I basically remember NOTHING correctly. It's a fun run, though, and this is the result of a couple hours' routing and a few more running. I bet sub-5 is possible if you super-optimize the coin grabs (and, of course, not mess up all the jumps I mess up).