distribution function with uniformity

I'm having trouble solving the following problem correctly:

The waiting time until delivery of a new component for an industrial operation is uniformly distributed over the interval 1 to 5 days. The cost of this delay is given by . Find the probability density function for .

so far I have:

and based on an example from the book I have:

then combining for the top part I would get:

and based on the solution in the back of the book it's:

if anyone can help me it it would be greatly appreciated