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A number that is a multiple of both 5 and 2 is also known as a multiple of 10.
The numbers that are multiples of 10 within the range of the spinner are 10.
There is 1 number that is a multiple of both 5 and 2 out of the 13 possible outcomes.
Therefore, the probability of spinning a number that is a multiple of 5 and a multiple of 2 is 1/13.