Write a program that asks the user for the name of a file. The program should display only the first five lines of the file's contents. If the file contains less than five lines, it should display the file's entire contents. This is what I have, please help.
```python
def file_head_display(limit=5):
file = str(input('Enter the name of the file: '))
f_open = open(file, 'r')
line_counter = 0
for line in f_open:
if line_counter < limit:
print(line, end="")
line_counter += 1
else:
break
file_head_display()
```