A can finish a work in $33$ days and B can finish the same work in one-third the time taken by A. Working together, what part of the same work can they finish in $5$ days?

Time taken by A $=33\text{ days}$.Time taken by B $=\frac{1}{3}\times 33=11\text{ days}$.Let's find their individual work rates per day:Work done by A in 1 day $=\frac{1}{33}$ Work done by B in 1 day $=\frac{1}{11}$ The combined work done by both together in 1 day is:
$${\text{Combined Work}}_{1\text{ day}}=\frac{1}{33}+\frac{1}{11}=\frac{1+3}{33}=\frac{4}{33}$$
The part of the work completed by them together in $5$ days is:
$${\text{Combined Work}}_{5\text{ days}}=5\times \frac{4}{33}=\frac{20}{33}$$