Answer
$6.5mJ$ (this answer can differ based on your estimated $\Delta x$ value)
Work Step by Step
Since the question asks for energy to compress a spring, use the elastic potential energy equation $$U=\frac{1}{2}k\Delta x^2$$ Let's assume that the button must be compressed $1.0cm$, which is $0.010m$ Substituting $\Delta x=0.010m$ and $k=130N/m$ yields an estimated energy of $$U=\frac{1}{2}(130N/m)(0.010m)^2=6.5mJ$$
