After you clear the fraction, expand the left side and then move all the terms that contain $m$ to one side of the equation and the terms without $m$ to the other.

Once you have something like $m(\text{something}) = \text{something with }k$, factor $m$ and then divide to solve for $m$ in terms of $k$.

In Desmos, type y = 5x/(x-3). This graphs the relationship between $k$ (on the y-axis) and $m$ (on the x-axis).

The algebraic solution gives $m = 3k/(k-5)$. Type y = 3x/(x-5) to see $m$ as a function of $k$, or verify by checking that swapping variables gives an equivalent relationship.

Pick a value of $k$ (not 5), find where it intersects y = 5x/(x-3), and verify that the x-coordinate matches 3k/(k-5) for your chosen $k$.

Start with the given equation:

To remove the denominator, multiply both sides by $(m-3)$:

Now there is no fraction, and you can work with a linear equation in $m$.

Distribute $k$ on the left side:

Now get all the $m$ terms on one side by subtracting $5m$ from both sides:

Both terms on the left now contain $m$.

Factor $m$ out of the left side:

Now isolate $m$ by dividing both sides by $(k-5)$ (this is allowed because the problem states $k \ne 5$):

So the correct equation expressing $m$ in terms of $k$ is $m = \dfrac{3k}{k-5}$, which corresponds to choice D.