Sum of Three Primes and Vinogradov's Theorem

Question

My course instructor told me that every odd number greater than $5$ is sum of three primes. However the following statement is confusing.

But there is a theorem by Vinogradov that states

There exists some X > 0 such that every integer n > X can be expressed as a sum of three odd primes.

So I am confused which of the following is correct. Is it true for all odd numbers greater than $5$ or only for sufficently large odd numbers?

Answer 1

Vinogradov only proved it for sufficiently large odd numbers, but this result is extended to all odd integers greater than 5 by Helfgott.