There is a spinner with 15 equal areas, numbered 1 through 15. If the spinner is spun one time, what is the probability that the result is a multiple of 5 or a multiple of 3?

The multiples of 5 on the spinner are 5 and 10, and the multiples of 3 are 3, 6, 9, and 12. The number 15 is both a multiple of 5 and a multiple of 3, but we only want to count it once. Therefore, there are a total of 6 possible outcomes that satisfy the condition. The probability of getting one of these outcomes is:

$$\frac{6}{15} = \frac{2}{5} = \boxed{0.4}$$

Therefore, the probability of getting a multiple of 5 or a multiple of 3 is 0.4.