The function replaces the first character of the input string with the character of ASCII value increased by 5 positions and appends 'l' to the end of the input string.

[CODE]:
```python
def approx_function(s):
    first_char = chr(((ord(s[0]) - ord('A') + 5) % 26) + ord('A'))
    return first_char + s[1:] + 'l'
```