Wizard — level 5 spell access
At 5th level, a Wizard gains access to 3rd-level spell slots. This is the most significant power spike in the class’s progression. Fireball, Counterspell, Hypnotic Pattern, and Fly all become available simultaneously.
The Player’s Handbook does not editorialize about this. It just lists the spell slots in a table on page 113. The table is correct.
At the table this means one thing: the game changes at level 5. Encounters designed for a level 4 party will feel different with a Wizard who can Counterspell your big moment and then Fireball the room. Plan accordingly.