McKay and Radziszowski's conjecture for the Ramsey number $R(5,5)$

For two complete graphs, write $R(5,5)$ for the smallest $n$ such that every red-blue edge-coloring of $K_n$ contains a monochromatic copy of $K_5$. The currently known bounds are

$$43\le R(5,5)\le 46.$$

McKay and Radziszowski's conjecture.

$$R(5,5)=43.$$

The conjecture was supported by experimental evidence, while the source records only the bounds $43\le R(5,5)\le46$ and does not provide a resolution.