Answer
$(0, 5)$
Refer to the graph below.
Work Step by Step
$x\lt5$ includes that numbers that are less than $5$.
$x\gt0$ includes that numbers that are greater than $0$.
The conjunction "and" means intersection so find the numbers that are common to both inequalities.
The intersection of the two given sets is the set of real numbers that are greater than $0$ but less than $5$.
Hence, the solution set is $(0, 5)$.
Graph the solution set by plotting holes at $0$ and $5$, the shade the region in between them. (Refer to the graoh above.)