Step 1: Understand what the xy-plane is.
The xy-plane is the flat sheet where the height $z$ is zero. So any point lying on it must have $z = 0$. We want the point where the segment joining the two given points crosses this sheet, and in what ratio it cuts the segment.
Step 2: Set up the section formula idea.
Suppose the xy-plane cuts the segment from $P(2,4,5)$ to $Q(3,5,-4)$ in the ratio $k : 1$. The $z$-value of the cutting point comes from the section formula.
\[ z = \frac{k(z_2) + 1(z_1)}{k + 1} \]
Step 3: Put in the z-values.
Here $z_1 = 5$ and $z_2 = -4$. The cutting point sits on the xy-plane, so its $z = 0$.
\[ 0 = \frac{k(-4) + 1(5)}{k + 1} \]
Step 4: Clear the fraction.
Since the bottom $k+1$ is not zero, the top must be zero.
\[ -4k + 5 = 0 \]
Step 5: Solve for $k$.
Move terms to get $4k = 5$, so $k = \frac{5}{4}$. This means the ratio is $5 : 4$.
Step 6: Decide internal or external.
A positive ratio means the cutting point lies between the two points, so the division is internal. A negative ratio would have meant external. Here $k = \frac{5}{4}$ is positive, so it is internal.
\[ \boxed{5 : 4 \text{ internally}} \]