Actually, imagine your leg at full extension. With longer cranks, your foot is 5mm further away. To maintain the same leg extension at the bottom of the stroke, you would lower the saddle with longer cranks. Excess leg extension could cause you an overuse injury with time.
Conversely, if you changed to a pedal with higher stack height, the pedal is now a bit closer to you at the bottom of the stroke. You would raise the saddle now, not lower it.
This is less important, but if you raise the saddle, it is now a few mm further back. So, some riders might move the saddle forward slightly. However, that more comes into play with major changes in your saddle height.
The other answer stated that 5mm changes may not be noticeable. I think there’s a consensus is that 5mm is about the minimum noticeable change in crank length. I would definitely change my saddle height. I have felt a difference going to a shorter crank and not moving the saddle, but I am pretty sensitive. The other answer is correct that many cyclists might not notice the change.
Astute readers might realize that if you move to a shorter crank and raise the saddle, at the top of the stroke, your foot is a bit less extended than it was previously, i.e. your hip angle at the top of the stroke will be a bit more open. If your position is low enough, you might have difficulty traveling over the top of the stroke. It's possible this may lead to hip impingement over time. Shorter cranks reduce the risk of this. Relatedly, you might get hip impingement if your saddle is too low, although I think it has to be quite a bit too low to do this.