Fit
Fitness
Efficiency of not changing body position to shift or brake
Proficiency anticipation and shifting
Higher cadence to minimize speed loss
= Faster

These can easily add up without you being acutely aware of them.
I can see 5 minutes over 21 miles, and I can see 8 minutes over 21 miles.
I can also see a 15% improvement, especially if gomango says it.
Like iab points out, it's hard to pin it all on the bike, and I see his point.

The people I help to get into triathlons all want to buy speed.
The vast majority don't get much faster when they do.
The ones that retain that "slow bike" see gradual improvement.
Then, when they buy that "fast bike," they see dramatic improvement.
It's not the bike, it's what the bike does for them:
1-It's always a better fit. They know what works this time around.
2-They're in better shape, and determined to go faster.
3-They're experienced as far as technique and often on more modern shifting.
4-They've stopped mashing.

All of the factors above were involved.

Many riders (and runners) see dramatic breakthroughs when they unwittingly make a mental change.
For cyclists, it can be bike change, easily, that removes a mental obstacle that was holding them back.
For runners, it's often a race where they lose track of their pace and outrun what they thought they could do.
I've seen 10K runners drop from 34's to mid 31's because they get caught up in a fast pack.
They realized they really didn't suffer all that much more, and gain confidence and get faster.

The exact same thing can happen with a bike change. Several factors combine to make you faster.
Because you went faster, you drop mental inhibitions that you had before, and you do get faster.
The initial drop of 5 minutes could easily have been the breakthrough.
The next drop of 3 more minutes could easily be because of your renewed vigor.

If you think you're faster, you often are, and you want to be able to point to a reason, when usually it's reason(s).
Take that effect, add in a better bike fit, better gearing, and better riding technique, dramatic improvement is definitely a possbility. If my trainees want to think it's their new bike, fine with me, but they're shortchanging themselves and their own efforts.