jmc

The sum of the interior angles of this pentagon is $(5-2)\cdot 180=540$ degrees. Thus, we have the equation $540=(x+1)+2x+3x+4x+(5x-1)\Rightarrow 540=15x\Rightarrow x=36$. The largest angle has measure $5x-1$, or $5\cdot 36-1=\boxed{179}$ degrees.