  The intensity mapping of the [CII] 157.7 $\rm \mu$m fine-structure emission
line represents an ideal experiment to probe star formation activity in
galaxies, especially in those that are too faint to be individually detected.
Here, we investigate the feasibility of such an experiment for $z > 5$
galaxies. We construct the $L_{\rm CII} - M_{\rm h}$ relation from observations
and simulations, then generate mock [CII] intensity maps by applying this
relation to halo catalogs built from large scale N-body simulations. Maps of
the extragalactic far-infrared (FIR) continuum, referred to as "foreground",
and CO rotational transition lines and [CI] fine-structure lines referred to as
"contamination", are produced as well. We find that, at 316 GHz (corresponding
to $z_{\rm CII} = 5$), the mean intensities of the extragalactic FIR continuum,
[CII] signal, all CO lines from $J=1$ to 13 and two [CI] lines are $\sim
3\times10^5$ Jy sr$^{-1}$, $\sim 1200$ Jy sr$^{-1}$, $\sim 800$ Jy sr$^{-1}$
and $\sim 100$ Jy sr$^{-1}$, respectively. We discuss a method that allows us
to subtract the FIR continuum foreground by removing a spectrally smooth
component from each line of sight, and to suppress the CO/[CI] contamination by
discarding pixels that are bright in contamination emission. The $z > 5$ [CII]
signal comes mainly from halos in the mass range $10^{11-12} \,M_\odot$; as
this mass range is narrow, intensity mapping is an ideal experiment to
investigate these early galaxies. In principle such signal is accessible to a
ground-based telescope with a 6 m aperture, 150 K system temperature, a
$128\times128$ pixels FIR camera in 5000 hr total integration time, however it
is difficult to perform such an experiment by using currently available
telescopes.
