Integer of form 6k + 5 is of form 3k + 2 but not Conversely

Theorem
Let $n \in \Z$ be an integer of the form:
 * $n = 6 k + 5$

where $k \in \Z$.

Then $n$ can also be expressed in the form:
 * $n = 3 k + 2$

for some other $k \in \Z$.

However it is not necessarily the case that if $n$ can be expressed in the form:
 * $n = 3 k + 2$

then it can also be expressed in the form:
 * $n = 6 k + 5$

Proof
Replacing $2 k + 1$ with $k$ gives the result.

Now consider $n = 8$.

We have that:
 * $8 = 3 \times 2 + 2$

and so can be expressed in the form:
 * $n = 3 k + 2$

However:
 * $8 = 6 \times 1 + 2$

and is in the form:
 * $n = 6 k + 2$

and so cannot be expressed in the form:
 * $n = 6 k + 5$