Use the number line and add the following integers: $( - 5) + 10$.

Hint: Two integers are given. One of them is positive and the other is negative. Therefore they will be on different sides of zero on the number line. Start with one of the numbers, say $10$. Then count to the left for five places to add $ - 5$.

Complete step-by-step answer:
Given the numbers $ - 5$ and $10$.
We can see these numbers will be on different sides of zero on the number line.
$ - 5$ will be five places left of zero and $10$ will be ten places right of zero.
We need to find their sum.

We can see the sum from the number line.
While adding we have to count towards right and while subtracting we have to count towards left.
But adding a negative number will effect in subtracting its magnitude.
So adding $ - 5$ is equivalent to subtracting $5$.
When adding $ - 5$ to $10$, the result becomes $5$ places left to 10, which is $5$.
So we have, $( - 5) + 10 = 5$

$\therefore $ The answer is $5$.

Note: In the question it is specified to use a number line to find the sum of the two numbers. If not, we can add in another way. To add a positive and a negative number, just take the difference between their magnitudes and put the sign of the greater number.
Here the numbers are $ - 5$ and $10$.
We can see the magnitudes or absolute values as $5$ and $10$. Difference of $5$ and $10$ is $5$. Also the greater number here has positive signs.
So we have, $ - 5 + 10 = 5$