voltage drop in circuit

Check all the places on the circuit where the line is cut. Like outlets etc. Make sure the contacts are solid.

If you find any aluminum wire.. BINGO. Have a professional check out all the wiring in your home.

It may just be normal for the washer.

All the neutrals in your main tight?

First off, you should have a 20A circuit for your washer. My washer pulls 11.1Amps (according to the nameplate). And it was made in October or November 2003. It's probably OK to put both the washer and dryer (if it's a gas dryer) on the same 20A circuit, but not recommended. Also not recommended is the putting the lights on the same circuit as the washer. Lighting curcuits should always be separate from non lighting so when you trip a breaker your lights don't go out also.

Now as to your specific problem, you are most likelly getting voltage drop either because of a bad connection or maybe because you are taxing the circuit to it's limit.

Do the lights flicker the whole time, or do they flicker when the motor comes on, and then stabilize? If its the whole time, you have a problem; if just when the motor comes on, probably not. (I am making an assumption you have florescent lights; incandescent should never flicker, though they might dim.)

You are seeing a voltage drop of 2.5v with the washer on. That is little more than 2% and nothing to worry about. If you actually have 5a and it is a 14 gauge cable, it means you have a 90' circuit. That is a bit on the long side, and you should avoid putting anything really heavy on it; but 5a is fine.

Has anyone looked at the length of run on the wire and wire diameter. for

I would say this is normal. Any decent electronics should be able the handle this. I would put a surge suppressor just to be safe though since you have a motor (source of noise and spikes) on the same line.