the sum of five consecutive numbers is 28 more than the sum of the third and the fifth numbers.find the consecutive numbers

let the numbers be

x-2 , x-1 , x , x+1, and x+2

x-2 + x-1 + x + x+1+ x+2= x + x+2 + 28
5x = 2x + 30
3x = 30
x = 10

the numbers are
8 9 10 11 and 12