Our understanding of the intergalactic medium at redshifts z = 5–6 has improved considerably in the last few years due to the discovery of quasars with z > 6 that enable Lyman-α forest studies at these redshifts. A realization from this has been that hydrogen reionization could end much later than previously thought, so that large ‘islands’ of cold, neutral hydrogen could exist in the IGM at redshifts z = 5–6. By using radiative transfer simulations of the IGM, we consider the implications of the presence of these neutral hydrogen islands for the 21-cm power spectrum signal and its potential detection by experiments such as HERA, SKA, LOFAR, and MWA. In contrast with previous models of the 21-cm signal, we find that thanks to the late end of reionization the 21-cm power in our simulation continues to be as high as Δ$\mathrm{<mrow\; data-mjx-texclass="ORD">21</mrow><mrow\; data-mjx-texclass="ORD">2</mrow>}$ = 10 mK$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$ at k ∼ 0.1 h cMpc$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ at z = 5–6. This value of the power spectrum is several orders of magnitude higher than that in conventional models considered in the literature for these redshifts. Such high values of the 21-cm power spectrum should be detectable by HERA and SKA1-low in ∼1000 h, assuming optimistic foreground subtraction. This redshift range is also attractive due to relatively low sky temperature and potentially greater abundance of multiwavelength data.