You may have realized that the the least common denominator is $\displaystyle{5}{m}\cdot{3}{n}={15}{m}{n}\usepackage{cmbright}\Huge\$ , but then incorrectly rewrote the fractions as: $\displaystyle\frac{{{5}{m}}}{{{15}{m}{n}}}-\frac{{{6}{n}}}{{{15}{m}{n}}}\usepackage{cmbright}\Huge\$

Instead, you should rewrite them using:

$\displaystyle\frac{{1}}{{{5}{m}}}-\frac{{2}}{{{3}{n}}}=\frac{{1}}{{{5}{m}}}\cdot\frac{{{3}{n}}}{{{3}{n}}}-\frac{{2}}{{{3}{n}}}\cdot\frac{{{5}{m}}}{{{5}{m}}}\usepackage{cmbright}\Huge\$

Multiply, and then subtract the numerators.