The positive integers less than or equal to $100$ that have no remainders when divided by $5$ are the multiples of $5$.
There are $100/5=20$ multiples of $5$ between $1$ and $100$.
The total number of positive integers less than or equal to $100$ is $100$.
The percentage of positive integers that have no remainders when divided by $5$ is $\frac{20}{100}=\boxed{20\%}$.
The answer is: 20
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
What percent of the positive integers less than or equal to $100$ have no remainders when divided by $5?$

### Answer:
