5. In a regular quadrilateral pyramid $P-ABCD$, the side faces are equilateral triangles with a side length of 1. $M, N$ are the midpoints of edges $AB, BC$ respectively. The distance between the skew lines $MN$ and $PC$ is $\qquad$.
Let $O$ be the midpoint of $A C$, $P O \perp$ base $A B C D \Rightarrow$ plane $P A C \perp$ base $A B C D$. Connect $O B$, intersecting $M N$ at $H$. Then $O B \perp$ plane $P A C \Rightarrow O H$ is the distance from line $M N$ to plane $P A C$, which is the distance between the skew lines $M N$ and $P C$. According to the problem, the side length of the base $A B C D$ is $1 \Rightarrow O H=\frac{\sqrt{2}}{4}$.