Is there any related non-parametric test that may combine the function of ANOVA and Post Hoc in a single run for replacing Duncan’s Multiple Range Test when there is need or necessity to treat small sample size statistically?
The nonparametric analog to a (one-way) ANOVA is the Kruskal-Wallis test. It can subsequently be re-run with subsets (as can individual Mann-Whitney tests). However, with a sample size of 5 cases, whether per group or overall, you will not have good statistical power to detect differences, unless those differences are enormous.