Can one use a current transformer of 1A for a 5A input
Current transformer 100 to 1, for example.line current 20 amp, current in secondary coil of current transformer will be 0.2 amp.
For transformer 100 to 5 ,line current 20 amp, current in secondary coil will be 1 amp.
5 amp input circuit will handle 0.2 amp without any problem, but it supposed to be graduated according to the high range of measurement -- highest possible line current. As in your question, you can use multiplier of 5 in case you replace current transformer with the same measurement range  e.g. (100 to 5) by (100 to 1). Other way you will overload input circuit.