import math

def is_prime(n):
    if n <= 1:
        return False
    for i in range(2, int(math.sqrt(n)) + 1):
        if n % i == 0:
            return False
    return True

def find_primes_starting_with_5():
    primes = []
    for num in range(500, 600):
        if str(num).startswith('5') and is_prime(num):
            primes.append(num)
    return primes

# Get all prime numbers with 3 digits starting with 5
primes_starting_with_5 = find_primes_starting_with_5()
print(primes_starting_with_5)