A box contains 15 marbles of which $x$ are green and the rest are yellow.

1. Express the number of yellow marbles and form the probability.

Number of yellow marbles $=15-x$.

$P(\text{yellow})=\dfrac{\text{number of yellow marbles}}{\text{total number of marbles}}=\dfrac{15-x}{15}$

1. Express the probability of choosing a yellow marble after 5 green marbles are added.

Initially, the number of yellow marbles is $15-x$.

After 5 green marbles are added, the total number of marbles is $15+5=20$.

Given that the new probability of choosing a yellow marble is $\dfrac12$,
$\frac{15-x}{20}=\frac12$

2. Solve the equation to find the initial number of green marbles.

$\frac{15-x}{20}=\frac12$
$15-x=10$
$x=5$

So the initial number of green marbles was $5$.