I guess you mean 17 amp-hour unit??
Capacity of battery is 12 V x 17 Ah = 204 Wh
Energy used by laptop is 15V x 5 A x 3h = 225 Wh
so if your figures are correct, you are doing very well with that powerpack. You are getting an extra 21 Wh of energy for free!

If you want the battery to last though (i.e. last many charge cycles) you should probably recharge it sooner, say before you drained 2/3 of the capacity, i.e. use laptop for 2 hours.
Capacity is proportional to amp-hour (Ah) rating, so you are correct that a 34 Ah battery will give you twice the energy as a 17 Ah one. Radio Parts have lead-acid batteries at very good prices in Melbourne.