Let the coefficients of x^$-$1 and x^$-$3 in the expansion of ${\left( {2{x^{{1 \over 5}}} - {1 \over {{x^{{1 \over 5}}}}}} \right)^{15}},x > 0$, be m and n respectively. If r is a positive integer such that $m{n^2} = {}^{15}{C_r}\,.\,{2^r}$, then the value of r is equal to __________.