Question
Thanks for your reply!  No, it is not under warranty - it was installed by the builder (former model home) and is several years old. Zone 1 has 5 pop-up heads; zone 5 also has 5 heads (all are non-rotary, a mix of 360, 245, 180 degree patterns). Not sure what you mean by "kind" of valves - manufacturer or...? I could describe them if you like; they're all in a valve box at a rear corner of the house. It seems like the thumping is happening when the valves open, since zone 1 is the first to activate. The controller is located in the garage, which is catty-corner to the location of the valve box. I hear the thumping in my office, which is adjacent to the garage on the same wall as the controller.
The water main entrance and sprinkler system tie-in are in the crawlspace below and about 20 feet away from the office. There are several insulated PVC water lines that run underneath the office to other parts of the house. The supply line to the valve box is copper, and it runs away from the office to the opposite corner of the house. Outside next to the valve box is a vertical copper pipe (about 1' high) with a white cap on top, a valve handle on the side, and a horizontal connection to the valve manifold. In the crawlspace, just after the main valve between the cold water supply and the sprinkler line, is a horizontal brass contraption about 2' long that has 2 valve handles on top and a circular portion with "Vent" printed on it; I believe this is a backflow prevention device? What the copper riser next to the valve box is, though, I'm not so sure. Please let me know what further info would help you - I'll pass on whatever I can!

Answer -
Liisa,
I have to ask the question is it still under warranty. Also tell me about zone 1 and 5. How many heads, what kind, what kind of valves in the ground. Is this a do it yourself system or put in by a contractor. When it starts the pipes bang, then when it finishes the pipes bang- so it the starting and stopping of water. Also, what kind of pipes are banging. Copper in the house,or a different kind of pipe.

Adjusting the flow knobs on the 1 and 5 valves might fix and that is pretty easy to do.  I need to know what kind of valves were installed

Answer
Liisa, OK we're making progress. But I need to know the brand of valve that are in the box. You have to open the lid off the thing and look at them and if you can't see the model (Toro, Rainbird, Hunter, etc..) Give me an idea what they look like. Also the brass valve I think is the backflow preventor. Can you give me a make and model off that? Or the valves in the ground in a box or are they above ground? And I'm not sure what the copper riser is unless it is a blowout for winterizing the system or something to connect a hose to. Jim