A model or order # will be on a sticker. On the bottom, or back side, or perhaps in the battery bay. I'm not a laptop owner, but it will be there somewhere.
Three PB 15" models could have been made in 2005. It's probably not the first one, but the date ranges are (barely) compatible.
order #s M9421LL/A (1.33 GHz) M9422LL/A (1.5 GHz)
OS X 10.3.3 - 10.5.8
PowerBook5,6 model A1106
order #s M9676LL/A (1.5 GHz) M9677LL/A (1.67 GHz)
OS X 10.3.7 - 10.5.8
PowerBook5,8 model A1138
order # M9969LL/A (1.67 GHz)
OS X 10.4.2 - 10.5.8