Movie 5: This COULD Work as being a camping trip they go on before training to fight the Cyborgs, if Piccolo not being with them in the beginning and Son not being able to go Super Saiyan on command is ignored. I personally don't count it as Canon for this reason. Son told Trunks when they spoke that he could now go SS on command.
I don't think that it was clear that he couldn't use Super Saiyan, I just thought it was plot induced stupidity and/or Goku knowing that a Freeza-level opponent by this point can be dealt with with just kaio-ken (Goku got a lot stronger from Yardrat and the android training), not expecting Cooler to be that strong. I mean, otherwise, no movie ever can ever work. Because in, for example, Movie 9, the one you say fits without problems, Trunks (maybe some others, haven't watched it in a while) waits until he gets the crapped kick out of him in base form before he gets really pissed off and goes Super Saiyan. Other than that one very minor thing, the movie seems to fit fine maybe a year after Trunks arrives. Also, Goku already has started training, Roshi says as much at the beginning of the movie.
It's purely dramatic effect. Really, it's a recurring theme in the movies. In Movie 7, the androids kick the crap out of the saiyans in base form, then rather than transform they just sit there and take it. Then, right as they're about to be finished off, THEN they go Super Saiyan. In Movie 10, Gohan shows up to fight Broly in base, and similar to Movie 7, he doesn't go Super Saiyan until he's about to die. In the former case, Goku doesn't even use kaio-ken. Though that's more of a problem with Movie 5's climax in general; I like the suggestion Gonstead made in the "If you could change the course/result of a fight..." thread:
Basically, Cooler would already be powerful enough to fend of Goku in the beginning without trying like he did when he transformed. Goku goes over the edge and turns SSJ to which he lands a beatdown upon Cooler. After that, Cooler would then announce that he had a form beyond the one he is seen in and proceed to transform.
After that, Cooler and Goku would fight with each other, each almost the same in power though Cooler is slightly more powerful, giving him an advantage over Goku.
The fight would go on for a while until they both step back, Goku is exhausted while Cooler looks perfectly fine. He describes his disappointment in the Super Saiyan and throws a ki blast at Goku, who blocks it which fills his vision with smoke. Cooler creates a Death Ball.
The rest is basically what was seen in the movie.