A 5 speed could have been either a cheapy or a specific time trial or similar
and cassettes are up to 11spd these days.
But that doesn't necessarily mean you'd get 33 useable gears. It does mean you'd get 11 sprockets with a minimal difference between for smoother changes but not all of them efficiently useable on a triple in the extreme positions (ie big sprocket on big chainring and small sprocket on small chainring. They'd probably go in but mechanically not good!)
'5 Speed' in the good old days was generally on a base model bike (before that it was 4 and before that 3) and a double chainset was an upgrade. Unless of course you were a time triallist and used 5 very close high gears - which is a different matter altogether.
EDIT - just seen your next post. It sounds like a time trial bike built for short distance events on flat courses where a wide choice of gears is unnecessary. 13 to 17 or 14 to 18 were common. In fact, very frequently only the top 2 or 3 were used. Alf Engers only had 3 sprockets fitted - and he generally used the smallest most of the time!
Today is the yesterday of tomorrow.