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.