What bike chain size do I buy?
Looks identical to an early 90s MTB I ride.   That too was 3x5 for 15 gears total.
I found that 6/7/8 speed chain worked well enough with the 5 gear freewheel.
But after decades of wear, the moving parts were a bit sloppy so when an opportunity arose, I fitted a 9 speed cassette and freehub wheel, with 9 speed chain/shifter/derailleur and its going nicely.  The bike still uses the original triple chainring and shifter, so theres a 9 position deore right hand shifter under the bar, and a friction twist shifter over the left side of the bar.