I believe the 5 beams project from within the structure.

I don't think the beams project from within since you can see a series of lag bolts attaching the pergola to the concrete above the garage door... These bolts would not be necessary if the beams were part of the structure of the house... I do believe that the wall on the right is the only support other than the lag bolts. Western cedar is a very light wood and so I have no trouble believing that this sparse structure would hold up just fine the way that it is... If I wanted to be absolutely certain though...I would run an iron cable from the front-left corner of the pergola straight up to the roof overhang of the house. It would be a nice complement to the style...especially since a wire handrail is located just beside the garage...nice match.

No, the beams project from within the building. This is called a cantilever. The distance inside the building is at least twice the distance of the projection