You need to go back to the definition of the cdf, which is
If y<0, then F(y)=0.
If 0<y<5, then you are correct,
HOWEVER, and it's good you check your work...
If 5<y<10, then =.5 + whatever.
And, for y>10, you better get 1, which I did, since this is a valid denisty.
That was the first thing I did, to see if it integrated to one.
Too often students write down incorrect 'densities' and I spend forever on the problem.