If each number can be used more than once and order matters, there are 714,924,299 different five-number combinations using one through 59. This is 59 x 59 x 59 x 59 x 59 because there are 59 different options for each of the five numbers slots.
This is called a permutation with repetition because each number can be used more than once and order matters. If each number, one through 59, can only be used once (a permutation without repetition), there are 600,766,320 combinations. If the order the numbers are in does not matter and there is no repetition (such as when lottery balls are picked), then there are 5,006,386 possible combinations.