Write a Python class Employee to manage employee details, including name$($public$),$ ID $($private$),$salary$($protected$)$ and years worked $($protected$),$ with functionality to apply a bonus of $5\%$ if the employee has worked more than $5$ years. Include all getters and setters along with additional function to modify salary based on the years worked and bonus.

Create $3$ instances for Employee class to test your code and these instances should be through user input.