  The cosmic microwave background $B$-mode signal is potentially weaker than
the diffuse Galactic foregrounds over most of the sky at any frequency. A
common method of separating the CMB from these foregrounds is via pixel-based
parametric-model fitting. There are not currently enough all-sky maps to fit
anything more than the most simple models of the sky. By simulating the
emission in seven representative pixels, we demonstrate that the inclusion of a
5 GHz data point allows for more complex models of low-frequency foregrounds to
be fitted than at present. It is shown that the inclusion of the CBASS data
will significantly reduce the uncertainties in a number of key parameters in
the modelling of both the galactic foregrounds and the CMB. The extra data
allow estimates of the synchrotron spectral index to be constrained much more
strongly than is presently possible, with corresponding improvements in the
accuracy of the recovery of the CMB amplitude. However, we show that to place
good limits on models of the synchrotron spectral curvature will require
additional low-frequency data.
