  The C-Band All-Sky Survey C-BASS is a high-sensitivity all-sky radio survey
at an angular resolution of 45 arcmin and a frequency of 4.7 GHz. We present a
total intensity 4.7 GHz map of the North Celestial Pole (NCP) region of sky,
above declination +80 deg, which is limited by source confusion at a level of
~0.6 mK rms. We apply the template-fitting (cross-correlation) technique to
WMAP and Planck data, using the C-BASS map as the synchrotron template, to
investigate the contribution of diffuse foreground emission at frequencies
~20-40 GHz. We quantify the anomalous microwave emission (AME) that is
correlated with far-infrared dust emission. The AME amplitude does not change
significantly (<10%) when using the higher frequency C-BASS 4.7 GHz template
instead of the traditional Haslam 408 MHz map as a tracer of synchrotron
radiation. We measure template coefficients of $9.93\pm0.35$ and $9.52\pm0.34$
K per unit $\tau_{353}$ when using the Haslam and C-BASS synchrotron templates,
respectively. The AME contributes $55\pm2\,\mu$K rms at 22.8 GHz and accounts
for ~60% of the total foreground emission. Our results suggest that a harder
(flatter spectrum) component of synchrotron emission is not dominant at
frequencies >5 GHz; the best-fitting synchrotron temperature spectral index is
$\beta=-2.91\pm0.04$ from 4.7 to 22.8 GHz and $\beta=-2.85\pm0.14$ from 22.8 to
44.1 GHz. Free-free emission is weak, contributing ~$7\,\mu$K rms (~7%) at 22.8
GHz. The best explanation for the AME is still electric dipole emission from
small spinning dust grains.
