Five classes of binomial/harmonic series of convergence rate $ -1/4 $

By applying the 'coefficient extraction method' to the symmetric transformation of hypergeometric series due to Chu and Zhang (2014), we examine systematically five classes of infinite series of convergence rate '$ -1/4 $' containing binomial coefficients and harmonic numbers. Numerous closed formulae in terms of universal constants (such as $ \pi $, $ \ln2 $, and the Riemann zeta values) are established.