When solving mixture questions, it can be useful to sketch the solutions with the ingredients SEPARATED.
8% of 5 liters = 0.4 liters. So, the original mixture contains 0.4 liters of salt

Let x = the volume (in liters) of 15% solution required
So, this solution contains 0.15x liters of salt

We get:


We want the resulting solution to be 10% salt.

In other words, we want: \(\frac{0.4 + 0.15x}{5+x}=\frac{10}{100}\) (aka 10%)

Simplify: \(\frac{0.4 + 0.15x}{5+x}=\frac{1}{10}\)

Cross multiply: \((10)(0.4 + 0.15x) = 5+x\)

Expand: \(4 + 1.5x = 5+x\)

Solve: \(x = 2\)

Answer: 2

Cheers,
Brent