  We measure the skewness power spectrum of the Cosmic Microwave Background
(CMB) anisotropies optimized for a detection of the secondary bispectrum
generated by the correlation of the CMB lensing potential with integrated
Sachs-Wolfe effect and the Sunyaev-Zel'dovich effect. The covariance of our
measurements is generated by Monte-Carlo simulations of Gaussian CMB fields
with noise properties consistent with Wilkinson Microwave Anisotropy Probe
(WMAP) 5-year data. When interpreting multi-frequency measurements we also take
into account the confusion resulting from unresolved radio point sources. We
analyze Q, V and W-band WMAP 5-year raw and foreground-cleaned maps using the
KQ75 mask out to l_max=600. We find no significant evidence for a non-zero
non-Gaussian signal from the lensing-secondary correlation in all three bands
and we constrain the overall amplitude of the cross power spectrum between CMB
lensing potential and the sum of SZ and ISW fluctuations to be 0.42 \pm 0.86
and 1.19 \pm 0.86 in combined V and W-band raw and foreground-cleaned maps
provided by the WMAP team, respectively. The point source amplitude at the
bispectrum level measured with this skewness power spectrum is higher than
previous measurements of point source non-Gaussianity. We also consider an
analysis where we also account for the primordial non-Gaussianity in addition
to lensing-secondary bispectrum and point sources. The focus of this paper is
on secondary anisotropies. Consequently the estimator is not optimised for
primordial non-Gaussianity and the limit we find on local non-Gaussianity from
the foreground-cleaned V+W maps is f_NL = -13 \pm 62, when marginalized over
point sources and lensing-ISW/SZ constributions to the total bispectrum.
