said by MIA_LEAK :I need to research carefully the HOA and code implications in my area before I start drilling holes in the side of my garage.
You need to do more than that.
The existing exhaust pipe routed up through the house also does not meet code.
Why?
Because it links the garage space with with interior of the home (even though where the vent pipe is run is behind drywall).
Now imagine a garage with a car idling and the dryer on - where do you think the carbon monoxide is going to go? It's going to get drawn into the dryer and then leak into the house through the unsealed ducting.
Without seeing an elevation drawing for the front/side of the house, can you run some approved-for-chimney-use B-vent vertically from the current - or a slightly different dryer location in the garage - to a point on the garage roof that's hidden from street view (ie. wouldn't run afoul of the HOA rules). Sorry I'm not looking at your floor plan drawing at the moment, so forgive me it it's evident that what I'm suggesting isn't possible.
What about coring the house wall 12" above the pavement beside the garage door frame and installing the dryer vent facing the street? Can you hide a vent behind a bush in that area?
Or if the house has a soffit at more or less the garage ceiling level, run the exhaust pipe up the inside garage wall, then over to the soffit, and then vent downwards through the soffit using a 'boot' and install a grill over the boot. All the while making sure that there is NO way for CO gas to leak into the house via your piping.