We can use the properties of logarithms to simplify this equation.

log5x = log5 1.5 + 1/3 log5 8

Using the property log a + log b = log ab, we can combine the logs on the right side:

log5x = log5 (1.5 * 8^(1/3))

Then we simplify the expression inside the logarithm:

log5x = log5 (1.5 * 2)

log5x = log5 3

Therefore, x = 3.