Problem, or Falacy?

A number $a$ can be expressed as the sum of two squares in two different ways. (I. e., $a=m^2+n^2=p^2+q^2$ for distinct positive integers $m, n, p, q, a$ ). When $m^2$ is divided by $n$ , the remainder is $5$ . When $n^2$ is divided by $m$ , the remainder is $2$ . Find the minimum value of the number $a$ .