Which part of California?

You can't make an asymmetrical home "look more symmetrical." If you want it to look good, you must coordinate with what you have. Not ignore its features and pretend it is something else.

The first update I'd do is remove the raised planter. The second is reconfigure and widen the walkway and landing at the entrance.

We can't really see what's near the entrance. It would be good if you could stand about 8' in front of the garage wall, in line with the front door and retake the pictures, but include another one taken from the same location that aims leftward and includes more space beyond the left of the house. The pictures would need to overlap slightly in order than we can see the complete scene without gaps. You need another picture, also in line with the front door, but taken from a good distance away ... probably from across the street. It should show the whole, or most of the front yard in a single picture.

The additional picture helps, but still need the ones taken from near where the walk curves.

btw, unless you do a lot of the work yourself, $5K is not going to get you very far :-)

I wouldn't remove all the lawn to replace everything because that would bring costs up. Hopefully the lawn is on two different systems and you can keep some and cut in planting for just an area. You could probably remove something like a 600 sq ft area and replace. If you are in socal let me know and I can direct you to a contractor that can help you..

Add a course of bricks to each side of the walkway which will match your drive and widen the walk. Remove white planters and grass between the walkway and the house, and plant the whole area between the house and walk with low shrubs or groundcovers or perennials; just be sure to keep them low so as not to interfere with the walkway.

I agree with the suggestions that adding interest to the left side rather than retaining all lawn there will help balance the property, though there won’t be symmetry because of the architecture. Add garden spaces on the left, whether substantial planting beds, trees or a planted patio; it needs to be something that will come out far enough to balance the mass of the garage.