Parts per million = (moles of solute)/(liters of solution) * 10^6
First, we need to find the number of moles of the solute, lithium bromide. Lithium bromide has a formula of LiBr, so we can conclude its gram-formula mass is 6.94+79.904=86.844 g/mol. This means that there are 5.8/86.844 = 0.0667864216 moles of lithium bromide.
So, the concentration in ppm is (0.0667864216)/(270) * 10^6 = 250 ppm (to 2 s.f.)