jmc

A five-digit palindrome would be of the form $ABCBA$, where $A$, $B$, and $C$ are digits (not necessarily distinct) from $0$ to $9$ (with $A$ from $1$ to $9$). We have three possibilities for each of $A$, $B$ and $C,$ which gives us $3^3=\boxed{27}$ possible palindromes.