Functions

If \(f''(x)=-f(x)\) and \(g(x)=f'(x)\) and \(\mathrm{F}(x)=\left(f\left(\frac{x}{2}\right)\right)^{2}+\left(g\left(\frac{x}{2}\right)\right)^{2}\) and given that \(\mathrm{F}(5)=5\), then \(\mathrm{F}(10)\) is equal to :