Learn Italian: Dopo cinque birre, l'uomo è ubriaco. - After five beers, the man is drunk.

When dopo (after) is followed by a noun, you do not need di. You generally only add di before a pronoun, like in dopo di me (after me) or dopo di lui (after him). Since cinque birre is a noun phrase, dopo alone is correct.

Does the adjective ubriaco change depending on who is drunk?

Yes. ubriaco is a regular adjective, so it must agree in gender and number with the noun it describes. If the subject were a woman, it would be la donna è ubriaca, and for multiple men, it would be gli uomini sono ubriachi.

Since the current lesson focuses on the subjunctive, why isn't it used here?

The subjunctive is triggered by uncertainty, emotion, or searching for a specific thing that might not exist (in a relative clause). This sentence is a simple, factual statement of reality (the man is already drunk), so it just uses the normal indicative mood (è).

Is there a verb form of ubriaco?

Yes, you can use the reflexive verb ubriacarsi to say 'to get drunk'. For example, if you wanted to say 'The man gets drunk easily', you would say L'uomo si ubriaca facilmente.