\[(5m - 3)(n + 1) - (2n + 3)(3 - 5m) =\]
\[= (5m - 3)(n + 1) + (2n + 3)(5m - 3) =\]
\[= (5m - 3)(n + 1 + 2n + 3) =\]
\[= (5m - 3)(3n + 4).\]