Friction shifters should work with any number of rear cogs. The number of cogs in back is usually determined by the space between the rear dropouts - 120mm = 5 or ultra 6, 126mm = 6 or 7, 130mm = 8,9,10. Some bikes are other sizes (eg 128 to handle either 126 or 130 hubs). Steel frames are commonly re-sized by bending the rear stays if their owners want to switch the number of gears. Just don't do this to an aluminum bike since aluminum doesn't tolerate being bent like steel.
Welcome to BF and hope that trash bike works out for you - I sure like mine
