Nancy is 5 yrs younger than her brother stan last year she was half as old as he was how old are they both

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

Nancy is 6, Stan is 11

Check:

Clearly they're five years apart.  Last year they were 5 and 10, half, good.