The function rotates each alphabetical character of the input string by 5 positions, keeping the case (uppercase, lowercase) the same. Numbers and special characters in the input string remain unchanged.

[CODE]:
```python
def rotate_characters(input_string, rotation=5):
    rotated_string = ""
    
    for char in input_string:
        if char.isalpha():
            shift = 65 if char.isupper() else 97
            rotated_string += chr((ord(char) - shift + rotation) % 26 + shift)
        else:
            rotated_string += char
            
    return rotated_string
```
Test the function with some inputs to ensure it approximates the implemented function f(x) properly.

COMMAND: PYTHON(./temp/function.py "AnotherTest" "Zebra123!" "ROTATE_m3")