Imagine replacing $(5a - 2)$ with a single letter, like $x$. Then your expression would look like $7x + 3x$. How would you combine those?

Once you combine the numbers multiplying the common part, rewrite the expression as a single number times $(5a - 2)$.

In Desmos, let $a$ act like $x$. Type f(x) = 7(5x - 2) + 3(5x - 2) to represent the original expression.

On new lines, type the answer choices with $a$ replaced by $x$: g(x) = 35x - 14, h(x) = 50x - 4, j(x) = 10(5x - 2), and k(x) = 10(5x - 4).

Look at the graphs: the function whose line lies exactly on top of $f(x)$ for all $x$ is equivalent to the original expression. You can also use a table in Desmos to compare $f(x)$ and each choice at several $x$-values; the equivalent expression will always give the same outputs as $f(x)$.

Look at the two terms in the expression:

Both terms have exactly the same parentheses $(5a - 2)$ multiplied by different numbers (7 and 3). This means $(5a - 2)$ is a common factor.

Since both terms contain $(5a - 2)$, factor it out just like you would factor $x$ from $7x + 3x$:

Now you have a single product with the sum of the coefficients outside the parentheses.

Add the numbers in the parentheses outside:

So the expression equivalent to $7(5a - 2) + 3(5a - 2)$ is $10(5a - 2)$, which matches answer choice C.