  We present the radio properties of 66 spectroscopically-confirmed normal
star-forming galaxies (SFGs) at $4.4<z<5.9$ in the COSMOS field that were [C
II] detected in the Atacama Large Millimeter Array (ALMA) Large Program to
INvestigate [C II] at Early times (ALPINE). We separate these galaxies
("CII-detected-all") into lower redshift ("CII-detected-lz", $\langle
z\rangle=4.5$) and higher redshift ("CII-detected-hz", $\langle z\rangle=5.6$)
sub-samples and stack multi-wavelength imaging for each sub-sample from X-ray
to radio bands. A radio signal is detected in the stacked 3 GHz image of
CII-detected-all and -lz samples at $\gtrsim3\sigma$. We find that the
infrared-radio correlation of our sample, quantified by $q_{\mathrm{TIR}}$, is
lower than the local relation for normal SFGs at $\sim$3$\sigma$ significance
level, and is instead broadly consistent with that of bright sub-mm galaxies at
$2<z<5$. Neither of these samples show evidence of dominant AGN activity in
their stacked Spectral Energy Distributions (SEDs), rest-frame UV spectra, or
X-ray images. Although we cannot rule out the possible effect of the assumed
spectral index and the applied infrared SED templates as at least partially
causing these differences, the lower obscured fraction of star formation than
at lower redshift can alleviate the tension between our stacked
$q_{\mathrm{TIR}}$s and that of local normal SFGs. It is possible that the dust
buildup, which primarily governs the IR emission in addition to older stellar
populations, has not had enough time to occur fully in these galaxies, whereas
the radio emission can respond on a more rapid timescale. Therefore, we might
expect a lower $q_{\mathrm{TIR}}$ to be a general property of high-redshift
SFGs.
