Yes, in the beginning, it is very normal to find yourself running to the washroom once you start drinking water on a regular basis. Our bodies will hold water if we aren't getting enough, and once we start getting it regularily, the body will release the stored water. So you aren't just getting rid of new water, you are flushing out old water as well. Once you get that regulated (a couple of days), your bathroom habits will settle down.
Of course, since you'll be drinking more than you were in the past, you will naturally go more than you were - but likely not five times in one morning.
Keep up the great work - you are doing wonderful!