You can run a ten speed chain on a 5 or 6 freewheel/ cassette. I've done it ..... am doing it.Hi Ray,
Just to help avoid any possible mismatch, if your Galaxy has, for example, 5 or 6 sprockets at the back, you won't be able to run a 10 speed chain on it sucessfully. You could, however, continue to run the original chain on the 10 speed crankset.
There is also a possible issue of bottom bracket axle length and chain line. I will send you a more detailed message tomorrow.
Tim
You can also run a 5/6)7/8 speed chain on narrower chainrings, but because of wider lateral space, you tend to get the chain slightly moving laterally and pinging the front mech on some gears. This doesn't affect the mechanics but it the tinkling can become annoying