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this question is really hard!
You need to know how many outcomes you have. Is the spinner composed of colors, numbers, names? What categories does the spinner have?
The sample space is {0, 1, 2, 3, 4, 5, 6}: all the possible value that "The number of heads" can take.
It all depends on what you do with the information that you note. If you count up the number of odds [or evens] in the five rolls, your sample space is {0,1,2,3,4,5} with size 6. If you look for whether you had more odds than evens your sample space is {Y,N}, with size 2. If you subtract the number of even outcomes from the number of odd outcomes, your sample space is {-5,-4,,...,4,5} which is of size 11.
The sample space consists of all the possible outcomes. A flip of a coin has 2 outcomes, H,T. The total number of outcomes for 6 flips are 26 or 64.