The warp 5 engine of the NX-01 could barely reach the speed of warp 5 and even when they did they could only maintain it for 15 minutes or so.

LAter on, yes. For some unknown (non-)reason. But in episode 1, they didn't seem to have any trouble reaching warp 5 and holding it for... basically as long as they wanted to.

Like I said, though, it needn't have been any contradiction. All they needed to do was say they needed to go warp 6.

It's a Warp 5 engine if it could go Warp 6 they would have called it the Warp 6 engine.

Exactly. If it's designed to do warp 5 - which it apparently did rather easily, such as in the first episode(s) - then needing to push it beyond that, maybe closer to warp 6, is an excuse for the ridiculous coal-fired-steam-locomotive type fires they had. What they did seemed to me more like Back To The Future, Part 3, than Star Trek.

To my knowledge they never go Warp 6 or Warp 5 for that matter ,the first time they were going for Warp 5 was in the episode "Fallen Hero" they would normally cruise with Warp speed 3 and in extreme circumstances Warp 4 so I don't know where you got the idea from that they would regularly fly with Warp 5? The fires were done for dramatic purpose and to create tension you know ...to entertain the viewer and not turning a tv show into a physics 101 program.

Then why not just have chug-chugging type sounds, as with the first Airplane movie that had propeller-plane noises for a jet?

You really have no concept of entertainment and appropriate content do you?,Trek is not comedy it is like a soap opera the only difference it is situated in space and the future and should be viewed as such nothing more or to use Gene Roddenberry's words "A Wagon Train To The Stars (i.e. a space western) .Airplane was a comedy and spoof on the disaster movies of the 70's in particular the Airport series with other iconic movies of the 70's blended in the mix.

Also, in the episode "Fight Or Flight" it's clearly stated that they're going warp 5, with no issues.

Sure they can go warp 5 but only for short periods which is what they showed in Fallen Hero.

Naw, they were cruising warp 5 in "Fight Or Flight."

Maybe it didn't need to travel so far and only had to stay at warp 5 for a short period,plus in Fallen Hero Enterprise was being chased and fired upon so probably energy otherwise needed for propulsion was rerouted for polarizing the hull for protection?

But Tucker said it was only warp 5 "on paper." We have multiple examples where that wasn't true. It was just bad writing consistency, a hallmark of all Trek shows. And all they had to do was say they needed to push it PAST warp 5 in that situation.

Also having FLAME coming out of stuff in Engineering, was just silly. They made it look like the nearly-exploding locomotive engine in Back To The Future III.

Are you an expert on Warp engines?

One doesn't need to be an expert to know that any kind of antimatter leak, for example, would result in huge explosions. Not smoke and flame.