let's convert the mixed fractions to improper fractions and the subtract.
[tex]\stackrel{mixed}{5\frac{3}{8}}\implies \cfrac{5\cdot 8+3}{8}\implies \stackrel{improper}{\cfrac{43}{8}} ~\hfill \stackrel{mixed}{3\frac{3}{4}}\implies \cfrac{3\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{15}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{43}{8}~~ - ~~\cfrac{15}{4}\implies \cfrac{(1)43~~ - ~~(2)15}{\underset{\textit{using this as the LCD}}{8}}\implies \cfrac{43-30}{8}\implies \cfrac{13}{8}\implies {\Large \begin{array}{llll} 1\frac{5}{8} \end{array}}[/tex]
