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We present a uniform analysis of 155 candidates from the second year of NASA's $K2$ mission (Campaigns 5-8), yielding 60 statistically validated planets spanning a range of properties, with median values of $R_p$ = 2.5 $R_\oplus$, $P$ = 7.1 d, $T_\mathrm{eq}$ = 811 K, and $J$ = 11.3 mag. The sample includes 24 planets in 11 multi-planetary systems, as well as 18 false positives, and 77 remaining planet candidates. Of particular interest are 18 planets smaller than 2 $R_\oplus$, five orbiting stars brighter than $J$ = 10 mag, and a system of four small planets orbiting the solar-type star EPIC 212157262. We compute planetary transit parameters and false positive probabilities using a robust statistical framework and present a complete analysis incorporating the results of an intensive campaign of high resolution imaging and spectroscopic observations. This work brings the $K2$ yield to over 360 planets, and by extrapolation we expect that $K2$ will have discovered $\sim$600 planets before the expected depletion of its on-board fuel in late 2018.