Yes, I understand your love or or bird, but 5-10 minutes out of his cage at a time? Thats crazy....not enough for any parrot. We all learn to watch our birds while we do other things around the house, it's no different than having a child, you watch them and do what you have to.
Also, a 12 x 12 cage is barely big enough for a parakeet. They need room to climb, and exercise their wings. Please get him a bigger cage, yes it's expensive, but you made the decision to home this innocent bird, and he deserves the best care, cage and attention from his family.