Knight's Tour on a 5 x 5 Board Start from any Square?

I'd just like to check my logic here...

I wrote code to solve the Knight's Tour and it works well for 8x8 boards starting the Knight at any square.

But... on a 5x5 board I show no solution possible when starting at square (0, 1).

What I tried for 5x5 starting the Knight at Row 0, Col 1:

1. Warnsdorff's path
2. Added Roth (tie breakers based on Euclidean distance from center).

Since those did not produce a solution I did code that is just basic recursion with backtracking to test every possible path -- also no solution found when starting a 5x5 on 1, 0.

I looked everywhere for a list of exhaustive solutions to the 5x5 board but found none.

Is it that there just is no solution for 5x5 when starting at square 0, 1?

Thank you!

Correct, there is no solution when you start at any of the squares adjacent to a corner square.