$f(x+2) = 5^{x+2} = 25\cdot f(x)$ e $f(x+1) = 5^{x+1} = 5\cdot f(x)$, logo: $f(x+2) - f(x+1)$ $=$ $25\cdot f(x)$ $-$ $5\cdot f(x)$ $=$ $\boxed{20\cdot f(x)}$ Alternativa $\mathbb{(C)}$