On 130mm 8 sp freewheels that was a real problem. On 126mm it wasn't nearly as common. It did happen but not often. Personally, I can't think of any reason to go from 5 to 7 sp. Unless you wanted an indexed shifter. You really don't gain anything. Good luck on whatever you choose.

PS, did you ever think about a SS/fixie. You're already at 120mm. Maybe you could sell the frame on ebay to a hipster and list it as a fixie ready ready vintage bike.