Since the ratio is a part to part ratio (5 to 3) just change it to a part to whole ratio, 5 hot drinks to 8 drinks total to make things easier first. Than divide 400 by 8 to see the scale factor which is 50. Finally multiply 5 times 50 to find out how much hot drinks there was total which is 250.
Ever seen this before:
5 hot drinks : 8 total drinks
x50 = x50 =
250 hot drinks : 400 total drinks