Good afternoon, the question in question is;

Now for my work, I started by writing f(t) as a sum of functions.Consider the piecewise function;

This can be written using step functions as :

______ + _______ .

The Laplace Transform is then: where

Where is the Heaviside Step function shifted by .

Now to take the Laplace transform of this, I am trying to use the Second Shift theorem on the second term,

But in my case, , so shifting it to the right by won't do anything to a horizontal line, so f(t)=5. So for my answer, I obtained:

Which is not showing as correct, I am not entirely sure where I am going wrong! Any help would be appreciated!