I know how to use the RANK function to return the rank of a number in
a list of numbers. However, is there a formula that will give me the
number (out of the list of numbers) that is a particular rank? For
example:

1) 1385
2) 6048
3) 5967
4) 7073
5) 5922

Is there a formula that I can type in a cell asking for the number
that is ranked #2 in the list above, and it will give 5922 as the
result?

Check out LARGE and SMALL
LARGE(array, k)