Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP.

\[ -{\left(t + 1\right)} {\left(t - 5\right)} {y'''} + 2 \, {y''} = {\left(t^{2} + 9\right)} y + t + 5 \hspace{2em} x( 4 )= -3 \]