Finite-size scaling behavior of the magnetization distribution for 5d Ising model

We have previously established that the magnetization distribution of the 5-dimensional Ising model can be fitted by a $p,q$-binomial distribution. Our extensive sampled Monte Carlo data can be used to determine the parameters' finite-size behavior. Now we use a long series expansion of the $p,q$-binomial coefficients to obtain finite-size scaling formulas not only for the Binder ratio and the susceptibility near $T_c$, but also for the entire magnetization distribution, including corrections-to-scaling terms.