Normally, when using Bull Rush you provoke an attack of opportunity from your target. Hammer to the Ground lets you make a Trip combat manuver after a successful Bull Rush. Will that trip also provoke? What if you take the option to attempt the trip without moving with your opponent? You take the -5 to trip, but does the enemy still get an attack of opportunity?
Yes, both the bull rush and the trip attempt, unless you have improved bull rush and/or improved trip, will provoke attacks of opportunity. The general rule of provoking always applies, unless there is a specific exception. Since Hammer to the Ground doesn't make a specific exception, it is safe to assume the general rule about combat maneuvers provoking attacks of opportunity still applies.