Q.Root system of Bailey Acacia
Our tree was planted as a young tree about 5 years ago. Our neighbor was told by her gardener that our tree killed her shrub that was about 30 years old. I believe it was a Photinia about 5 feet tall. Do the roots of our Acacia grow down deep or spread out?

The root system of the Acacia Tree is both shallow and runs deep.
They are know for their fast growing and invasive root system.
Whether or not the roots killed off another tree is difficult to say, but is possible.
Here are some articles with more information.
https://www.gardeningknowhow.com/ornamental/trees/acacia/acacia-tree-types.htm
https://www.gardeningknowhow.com/ornamental/trees/tgen/problem-tree-roots.htm