Answer:
I agree with you that step 5 doesn't make sense.
In step 4 he had accurately determined that there were 216 British and Indian stamps.
B = number of British stamps
N = number of Indian stamps (using N because "I" looks too much like a "1")
B + N = 216
3/5B = N
substitute for N:
B + 3/5B = 216
8/5B = 216
divide both sides of the equation by 8:
1/5B = 27
multiply both sides of the equation by 5:
B = 135
N = 81
It appears that step 5 is missing the "multiply by 5".