No. If you look at a bike fit, the first point you adjust when you get on the bike is the riders position in relationship to the bottom bracket, then everything else is adjusted from that central point. In other words, leave the saddle alone.

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"Suddenly the thought struck me. My floor is someone elses ceiling"-Nils Ferlin

I would think that if you want to lower the bars and maintain the same hip and arm angles, then you would be riding steeper.
So saddle forward... But IANAF

Like Jan said, saddle height and fore/aft is a done deal. 5mm, you'll prob be just fine but if anything changes oh so slightly, your reach to bars just increased by virtue of the headtube angle. 5mm is pretty slight. I'd be inclined to think you're good to go w no additional adjustments.

Don't move the saddle and see how it feels first. Then maybe slightly forward.

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Member of the Litespeed Factory Team
www.litespeed.com

Assuming a TT bike...

You move the aero bars and pads back a very small amount. (I could trig it but I'm too lazy to do the math right now)

However, if you think of your body position as fixed and that it rotates around a point anchored at the pedal (which is the correct way to do it), then theoretically you would roll the entire body forward and down by removing the spacer, which would indeed move the seat forward (and up) slightly. That assumes that you were set up nearly perfectly to start with, which is unlikely. Plus, 5 mm isn't much of a change on the front.

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"...the street finds its own uses for things"

Negative and sorry for not saying so first. This is ROAD bike. A Cannondale SuperSix.

No matter what bike ....the steerer angle brings your bars more forward the lower you go. Like others said in your case I wouldn't do anything to the seat.

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-shoki

At a 73deg head tube angle, I think the horizontal movement is 1/3 of the vertical. So dropping the bars 5mm moves them forward less than 2mm, not enough to notice.