Hello, nothing is better than having the vehicle lifted and the front end shaken down by a technician who can see what parts are loose or worn. Yes, could be ball joints, tie rod ends, wheel bearings, shock absorbers and / or mounts, stabilizer bar links, bushings, engine and transmission mounts and on and on. The transaxle is often referred to as an automatic transmission -- but this is a front wheel drive or all wheel drive vehicle, and the differential for the front driven wheels is integrated. I don't expect the noise is coming from there.
RepairPal Certified shops can diagnose and repair your 2005 Chevrolet Equinox. They provide transparent pricing with a minimum 12-month or 12,000-mile warranty on repairs and services.