More coins

You have coins of values $1$, $4$ and $5$. What is the smallest number of coins needed form the sum $x$ exactly?

In this task, $1 \le x \le 10^{100}$, i.e., $x$ can be very large. The algorithm should be efficient in all cases.

In a file morecoin.py, implement a function count that returns the smallest number of coins.

def count(x):
    # TODO

if __name__ == "__main__":
    print(count(8)) # 2
    print(count(12345)) # 2469
    print(count(1337**9)) # 2730314408854633746890878156