Hi Teo,
Yes, it does mean that. He'd actually be able to cast 5th level Spells... maybe more.
However, upon leveling... you do not get to choose any spells.
So if your entering a new circle of spells... ie 4th Level Spells... you will not learn any new spells. You can only use spells you have discovered/learned along the way.
The Improved SpellCasting also means.. for example... it will class the SpellSword level as an additional Wizard level.
So a Level 5 Wizard/ Level 1 SpellSword will be casting as a Level 6 Wizard. This effects the likes of most damage spells ( Fireball ..etc ) and Stoneskin/ Greater Magic Weapon... etc...etc