Casey was twice as old as his sister 3 years ago. now he is 5 years older than his sister. how old is casey?

Let x is Casey's sister age.
3 years ago: 
Casey was twice as old as his sister: 2a - 3
Now: 
he is 5 years older than his sister: a + 5

2a - 3 = a + 5
subtract a to both sides
2a - 3 -a = a + 5 - a
simplify
a - 3 = 5
add 3 to both sides
a - 3 + 3 = 5 + 3
simplify
a = 8

His sister age is 8 years old now.
Now: 
he is 5 years older than his sister: a + 5 = 8 + 5 = 13

proof: 
so 3 years ago,
his sister age: 8 - 3 = 5
Casey age 3 years ago:
13 - 3 = 10 (Casey was twice as old as his sister 3 years ago)


Casey is 13 years old now.