The answer is the first choice, "The library opens at 10:00 a.m. Saturday."
The colon in the second choice is misplaced. The colon should be placed between the 5 and the 0 in 500.
The colon after the word library in the third choice is not needed.
Instead of a colon being used to display the time in the fourth choice, a semi-colon is used, which is incorrect.