I am chuckling because I had this very debate with my husband only when I was pregnant and we "argued" about how many months pregnant I was...was I 9 or 10 months???
So your baby was born on August 15, 2007. On September 15, 2007, he would be ONE month old...on October 15, 2007 he'd be TWO months old and so on. It's perfectly OK to count his age by weeks, if you choose. Personally, I don't see a problem with telling someone that my baby is 5 weeks and 4 days old. At no other time in our lives are we proud to announce that we are weeks old so enjoy this opportunity. I think most parents stop calculating the weeks sooner than later and simply say, "He is 4 1/2 months old." It's your choice, what feels right to you.