  We have searched for HI 21cm absorption toward the two brightest radio AGN at
high redshift, J0924--2201 at $z = 5.20$, and J0913+5919 at $z=5.11$, using the
Giant Meter Wave Radio Telescope (GMRT). These data set a 3$\sigma$ upper limit
to absorption of $< 30%$ at 40 km s$^{-1}$ resolution for the 30 mJy source
J0913+5919, and $< 3%$ for the 0.55 Jy source J0924--2201 at 20 km s$^{-1}$
resolution. For J0924--2201, limits to broader lines at the few percent level
are set by residual spectral baseline structure. For J0924--2201 the column
density limit per 20 km s $^{-1}$ channel is: N(HI) $< 2.2\times 10^{18} \rm
T_s$ cm$^{-2}$ over a velocity range of -700 km s$^{-1}$ to $+1180$ km s$^{-1}$
centered on the galaxy redshift determined through CO emission, assuming a
covering factor of one. For J0913+5919 the column density limit per 40 km
s$^{-1}$ channel is: N(HI) $< 2.2\times 10^{19} \rm T_s$ cm$^{-2}$ within $\pm
2400$ km s$^{-1}$ of the optical redshift. These data rule out any cool, high
column density HI clouds within roughly $\pm 1000$ km s$^{-1}$ of the galaxies,
as are often seen in Compact Steep Spectrum radio AGN, or clouds that might
correspond to residual gas left over from cosmic reionization.
