5. Given $A(4,0), B(2,2)$ are points inside the ellipse $\frac{x^{2}}{25}+\frac{y^{2}}{9}=1$, and $M$ is a moving point on the ellipse, then the maximum value of $|M A| + |M B|$ is $\qquad$ .
5. $10+2 \sqrt{10}$ Detailed Explanation: From the problem, we know that $A$ is the right focus of the ellipse. Let the left focus of the ellipse be $F$, then
$|M A|+|M B|=10-|M F|+|M B| \leqslant 10+|B F|=10+2 \sqrt{10}$. The maximum value is achieved when $M$ is at the intersection of the ray $B F$ and the ellipse.