The mean free path of ionizing photons, λ
mfp, is a critical parameter for modeling the intergalactic medium (IGM) both during and after reionization. We present direct measurements of λ
mfp from QSO spectra over the redshift range 5 < z < 6, including the first measurements at z ≃ 5.3 and 5.6. Our sample includes data from the XQR-30 VLT large program, as well as new Keck/ESI observations of QSOs near z ∼ 5.5, for which we also acquire new [C ii] 158 μm redshifts with ALMA. By measuring the Lyman continuum transmission profile in stacked QSO spectra, we find
λ
mfp
=
9.33
−
1.80
+
2.06
,
5.40
−
1.40
+
1.47
,
3.31
−
1.34
+
2.74
, and
0.81
−
0.48
+
0.73
pMpc at z = 5.08, 5.31, 5.65, and 5.93, respectively. Our results demonstrate that λ
mfp increases steadily and rapidly with time over 5 < z < 6. Notably, we find that λ
mfp deviates significantly from predictions based on a fully ionized and relaxed IGM as late as z = 5.3. By comparing our results to model predictions and indirect λ
mfp constraints based on IGM Lyα opacity, we find that the evolution of λ
mfp is consistent with scenarios wherein the IGM is still undergoing reionization and/or retains large fluctuations in the ionizing UV background well below redshift 6.