We'll call the ages n and s
Nancy is 5 yrs younger than her brother Stan
n = s - 5
Last year she was half as old as he was
n - 1 = (1/2) ( s - 1 )
We substitute for n
s - 5 - 1 = (1/2) (s - 1)
2s - 12 = s - 1
s = 11
n = s - 5 = 6
Answer: Nancy is 6, Stan is 11
Check:
Clearly they're five years apart. Last year they were 5 and 10, half, good.