Is a 50-foot 14-gauge extension cord okay for a 15-amp load?

It’s borderline. You’ll drop about 3.3% of voltage, which is right at the 3% code recommendation. For finicky power tools, you might notice stalling under load; lights will dim slightly. Bumping up to 12 gauge drops loss to about 2% — safer and better for your tools. Don’t push it past 15 amps on a 14-gauge cord this long.