Recent observations have positioned the end point of the Epoch of Reionization (EoR) at a redshift of $z 5.3$. However, observations of the Lyman-alpha forest have not yet been able to discern whether reionization occurred slowly and late, with substantial neutral hydrogen persisting at a redshift of $ 6$, or rapidly and earlier, with the apparent late end driven by the fluctuating ultraviolet background. Gunn-Peterson (GP) absorption troughs are solid indicators that reionization is not complete until $z=5.3$, but whether they contain significantly neutral gas has not yet been proven. We aim to answer this question by directly measuring, for the first time, the neutral hydrogen fraction ($x_ HI $) at the end of the EoR ($5 z 6$) in high-redshift quasar spectra. For high neutral fractions, $x_ HI GP troughs exhibit damping wing (DW) absorption extending over $1000$ km $ beyond the troughs. While conclusively detected in Lyman-alpha emission lines of quasars at $z DWs are challenging to observe in the general Lyman-alpha forest due to absorption complexities and small-scale stochastic transmission features. We report the first successful identification of the stochastic DW signal adjacent to GP troughs at redshifts of $z=5.6$ through careful stacking of the dark gaps in the Lyman-alpha forest (S/N$=6.3$). We use the signal to present a measurement of the corresponding global $x_ HI )$ at $1 at $z=5.6$ and a limit of $x_ HI <0.44$ at $z=5.9$. The detection of this signal demonstrates the existence of substantially neutral islands near the conclusion of the EoR, unequivocally signaling a late-and-slow reionization scenario.