Example 1
Lane won fifth place in a Ryan Gosling lookalike contest.
In this handsome sentence, fifth is an ordinal adjective that indicates Lane's position in the contest, meaning that there were four men more Gosling-y than he.
Example 2
Natalie's first car was a teal 1993 Ford Tempo.
Here, first is an ordinal adjective that modifies the noun car in order to show that Natalie's busted old Ford was number one in her series of automobiles.
Example 3
Maine was the twenty-third state admitted to the Union.
In this example, twenty-third is an ordinal adjective that notes Maine's position in the series of territories that became part of the United States. Before Maine became a state on March 15, 1820, it was part of Massachusetts…which explains all of the Mark Wahlberg fans in Portland.