Yahtzee with Buddies Odds

What are the odds of getting a yahtzee with one roll?

1/6 * 1/6 * 1/6 * 1/6 * 1/6 = 1 out of 7,776

or is it:

1/6 * 1/6 * 1/6 * 1/6 = 1 out of 1,296

Since we don't have to worry about getting the first number.  It can be any of the 1 through 6.  We just have to match the next 4 numbers.