No.
Gogeta, the fusion of super saiyan 4 Goku and Vegeta.
When he was in the Hyperbolic Time Chamber training to beat Cell. I think he became Super Saiyan 2 after he died to save the world from Cell. If Goku could turn Super Saiyan 2 he would have beaten Cell himself, instead of making ohan fight him.
after goku summon shenron
Goku does not turn super saiyan 6 or 5 in fact. and it only goes up to super saiyan 3 in the manga and super saiyan 4 in the cartoon.
There is no such thing as a super saiyan 5.
Episode 230 "Super Saiyan 3"
No, he can't
yes
Yes, Goku turned into a super saiyan 4 when he was fighting Baby Vegeta in Dragoball GT
When Krillin was exploded by Frieza, Goku became angry and he went Super Saiyan.
Majin Goku
in Dragon ball AF he turn in to super saiyan 5