On polynomials, the least deviating from zero in $L[-1,1]$ metric, with five prescribed coefficients

The properties of polynomials $R_{n+5}(x)$, the least deviating from zero in $L[-1,1]$ metric with five given leading coefficients, whose forms were calculated earlier, are studied. Theorems 1, 2 with Theorem A contain a final classification of polynomials $R_{n+5}(x)$, whose number of sign changes in $(-1,1)$ is exactly equal to $(n+1)$.