First, multiply $-7$ by $2m$. What do you get for the coefficient of $m$?

Next, multiply $-7$ by $-5$. What is the sign of the result when you multiply two negative numbers?

After finding both products, write them together as a sum. Which answer choice matches that expression?

In Desmos, type f(m) = -7(2m-5) to represent the original expression as a function of $m$.

Type each option as its own function, for example g(m) = 14m-35, h(m) = -14m-35, j(m) = -9m+5, and k(m) = -14m+35. Look at the graphs: the line that lies exactly on top of the graph of $f(m)$ for all $m$ (same line everywhere) corresponds to the equivalent expression.

Use the distributive property, which says $a(b+c)=ab+ac$. Here, you have $-7(2m-5)$, so you need to multiply $-7$ by each term inside the parentheses: $2m$ and $-5$.

Multiply $-7$ by $2m$:

$-7 \cdot 2m = -14m$.

So the first term in the expanded expression is $-14m$.

Now multiply $-7$ by $-5$:

$-7 \cdot (-5) = 35$.

A negative times a negative gives a positive, so this second term is $+35$.

Put the two terms together from the previous steps: the expression becomes

$-14m + 35$.

So the expression equivalent to $-7(2m-5)$ is $\boxed{-14m+35}$.