let's firstly convert the mixed fractions to improper fractions and then sum them up.
[tex]\stackrel{mixed}{5\frac{3}{8}}\implies \cfrac{5\cdot 8+3}{8}\implies \stackrel{improper}{\cfrac{43}{8}}~\hfill \stackrel{mixed}{2\frac{3}{4}}\implies \cfrac{2\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{11}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{43}{8}+\cfrac{11}{4}\implies \cfrac{(1)43~~+~~(2)11}{\underset{\textit{using this LCD}}{8}}\implies \cfrac{43+22}{8}\implies \cfrac{65}{8}\implies 8\frac{1}{8}[/tex]
