let's firstly convert the mixed fractions to improper fractions, and then subtract.
[tex]\bf \stackrel{mixed}{5\frac{1}{4}}\implies \cfrac{5\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{21}{4}}~\hfill \stackrel{mixed}{3\frac{2}{3}}\implies \cfrac{3\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{11}{3}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{21}{4}-\cfrac{11}{3}\implies \stackrel{\textit{we'll use the LCD of 12}}{\cfrac{(3)21-(4)11}{12}}\implies \cfrac{63-44}{12}\implies \cfrac{19}{12}\implies 1\frac{7}{12}[/tex]
