  Let $k\subset S^3$ be a nontrivial knot. The Cabling Conjecture of Francisco
Gonz\'alez-Acu\~na and Hamish Short posits that $\pi$-Dehn surgery on $k$
produces a reducible manifold if and only if $k$ is a $(p,q)$-cable knot and
the surgery slope $\pi$ equals $pq$. We extend the work of James Allen Hoffman
to prove the Cabling Conjecture for knots with bridge number up to $5$.
