def all_primes(max_num):
    is_prime = [True] * (max_num + 1)
    p = 2
    while (p * p <= max_num):
        if is_prime[p]:
            for i in range(p * p, max_num + 1, p):
                is_prime[i] = False
        p += 1
    return [p for p in range(2, max_num + 1) if is_prime[p]]

def filter_primes_starting_with_5(primes):
    return [prime for prime in primes if str(prime).startswith('5')]

three_digit_primes = all_primes(999)
three_digit_primes = [p for p in three_digit_primes if p >= 100]

primes_starting_with_5 = filter_primes_starting_with_5(three_digit_primes)

print(primes_starting_with_5)