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.
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Episode 230 "Super Saiyan 3"
Episode 214: Vegeta's Pride. Goku turns to USSJ (Ultra Super Saiyan) and USSJ2 in the Hyperbolic Time Chamber. He turns to SSJ2 while fighting Majin Vegeta.
35. goku's ascension
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Goku goes super saiyan 3 episode 246 in dragon ball z the episode name is super saiyan 3?! So its kinda hard to miss