  We analysed 68 candidate planetary systems first identified during Campaigns
5 and 6 (C5 and C6) of the NASA \textit{K2} mission. We set out to validate
these systems by using a suite of follow-up observations, including adaptive
optics, speckle imaging, and reconnaissance spectroscopy. The overlap between
C5 with C16 and C18, and C6 with C17, yields lightcurves with long baselines
that allow us to measure the transit ephemeris very precisely, revisit single
transit candidates identified in earlier campaigns, and search for additional
transiting planets with longer periods not detectable in previous works. Using
\texttt{vespa}, we compute false positive probabilities of less than 1\% for 37
candidates orbiting 29 unique host stars and hence statistically validate them
as planets. These planets have a typical size of $2.2R_{\oplus}$ and orbital
periods between 1.99 and 52.71 days. We highlight interesting systems including
a sub-Neptune with the longest period detected by \textit{K2}, sub-Saturns
around F stars, several multi-planetary systems in a variety of architectures.
These results show that a wealth of planetary systems still remains in the
\textit{K2} data, some of which can be validated using minimal follow-up
observations and taking advantage of analyses presented in previous catalogs.
