Binomial Theorem

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 __________.