If there are 5 ways to perform task $A$ and 8 ways to perform task $B$, then how many ways are there to perform task $A$ and then task B? There are ways to perform task $A$ and then task $B$.

Step 1 ：The problem is asking for the total number of ways to perform two tasks, task $A$ and task $B$, in sequence. This is a combinatorics problem, and the principle of multiplication applies here. According to this principle, if there are $m$ ways to do one thing, and $n$ ways to do another, then there are $m \times n$ ways to do both.

Step 2 ：In this case, there are 5 ways to perform task $A$ and 8 ways to perform task $B$. So, the total number of ways to perform both tasks is $5 \times 8$ which equals to 40.

Step 3 ：Final Answer: \(\boxed{40}\)