Then, what does that make 119 with respect to those moduli? -1, right? Meaning that 2, 3 ,4 and 5 cannot divide 119 evenly. But, by the unique factorization theorem we know that 119 has prime divisors, either 119 if 119 is prime (it isn't) or some combination of primes, each of which is greater than n = 5.
In this case, the divisors of 119 are 7 and 17. 7 > 5. 17 > 5.
I'm using 5 here for demonstration purposes, but hopefully it is plain to see that it doesn't matter what n is. The same logic will hold.