Here's a step-by-step to answering this question:
[tex]2 \frac{1}{2} + 3 \frac{1}{3} = \frac{5}{2} + \frac{10}{3} [/tex]
Then we need to find a lowest common denominator (in this case, its six):
[tex]\frac{5}{2} + \frac{10}{3} = \frac{15}{6} + \frac{20}{6} = \frac{35}{6}[/tex]
Now we add and simplify:
[tex]\frac{15}{6} + \frac{20}{6} = \frac{35}{6}[/tex]
[tex]\frac{35}{6} = 5 \frac{5}{6} [/tex]