sixty-fifth vs 65th

sixty-fifth and 65th both are adjectives.

Word	Noun	Adjective	Verb	Adverb
sixty-fifth	No	Yes	No	No
65th	No	Yes	No	No

As adjectives, sixty-fifth and 65th are synonyms defined as:

sixty-fifth and 65th: the ordinal number of sixty-five in counting order

sixty-fifth (adjective)	65th (adjective)
the ordinal number of sixty-five in counting order	the ordinal number of sixty-five in counting order