differential equations - How to solve Laplace transform question for a system in Mathematica

I know how to use the LaplaceTransform function but am struggling to do this with a system with two ODEs.

This is my question:

Use Mathematica and the Laplace transform method to solve the system: $$\begin{cases}f^\prime&=3f+5g-\sin(x)\\g^\prime&=2f-g+\cos(x)\end{cases}$$ with initial conditions $f(0)=0$ and $g(0)=1$