How many 5 number combinations are there and what are they?

1) if you mean using just the 5 digits 1,2,3,4,5

a) If you are allowed to repeat the numbers, like if it's okay to put 55555, then it's 5 x 5 x 5 x 5 x 5 = 3,125.  ANSWER  b) If you can't repeat the numbers then it's 5 x 4 x 3 x 2 x 1  = 120                    ANSWER

If you mean using all 10 digits but with just 5 places

a) If you can repeat 10 x 10 x 10 x 10 x 10 = 100,000    ANSWER 

b) if you can't repeat 10 x 9 x 8 x 7 x 6 = 30,240      ANSWER