We present time-resolved near-infrared spectroscopy of two L5 dwarfs, 2MASS J18212815+1414010 and 2MASS J15074759-1627386, observed with the Wide Field Camera 3 instrument on the Hubble Space Telescope (HST). We study the wavelength dependence of rotation-modulated flux variations between 1.1 $mu$m and 1.7 $mu$m. We find that the water absorption bands of the two L5 dwarfs at 1.15 $mu$m and 1.4 $mu$m vary at similar amplitudes as the adjacent continuum. This differs from the results of previous HST observations of L/T transition dwarfs, in which the water absorption at 1.4 $mu$m displays variations of about half of the amplitude at other wavelengths. We find that the relative amplitude of flux variability out of the water band with respect to that in the water band shows a increasing trend from the L5 dwarfs toward the early T dwarfs. We utilize the models of Saumon & Marley (2008) and find that the observed variability of the L5 dwarfs can be explained by the presence of spatially varying high-altitude haze layers above the condensate clouds. Therefore, our observations show that the heterogeneity of haze layers - the driver of the variability - must be located at very low pressures, where even the water opacity is negligible. In the near future, the rotational spectral mapping technique could be utilized for other atomic and molecular species to probe different pressure levels in the atmospheres of brown dwarfs and exoplanets and uncover both horizontal and vertical cloud structures.
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