The function takes an input string and shifts each alphabetical character by 5 positions forward in the alphabet, wrapping around when it reaches the end of the alphabet. The case of the character is preserved, and non-alphabetical characters remain unaltered.

[CODE]: 
```python
def shift_string_by_five(input_str):
    output_str = ""
    for char in input_str:
        if 'a' <= char <= 'z':
            output_str += chr(((ord(char) - ord('a') + 5) % 26) + ord('a'))
        elif 'A' <= char <= 'Z':
            output_str += chr(((ord(char) - ord('A') + 5) % 26) + ord('A'))
        else:
            output_str += char
    return output_str
```