5. The minimum value of the function $y=\sqrt{x^{2}-2 x+5}+\sqrt{x^{2}-4 x+13}$ is $\qquad$
5. $\sqrt{26}$

Hint: $y=\sqrt{(x-1)^{2}+(0-2)^{2}}+\sqrt{(x-2)^{2}+(0-3)^{2}}$, which can be seen as the sum of the distances from the point $(x, 0)$ to $(1,2)$ and $(2,3)$. By symmetry, the minimum value is easily found to be $\sqrt{26}$.