While it’s good for kids to practice being responsible for another being (someday, they’ll have to at minimum be responsible for themselves), make sure that YOU want a dog and the responsibility of that dog for when the kid is sick, busy with school/sports/studying/etc. in a few years, at camp, loses interest, etc. If you are having qualms, don’t do it.
I agree with the disagreement about the “Dog Whisperer”. His methods are suboptimal and, at times, downright dangerous to the dog and himself (he has been bitten far more times than the typical veterinarian gets bitten in their entire career, and given how many dogs are terrified at the vet, that should tell you something), and for a new dog owner to attempt to use them is asking for someone to get hurt and the dog end up back at the shelter or worse. If police dogs can be trained with only positive reinforcement and no punishment (and they can), and if behaviorists can rehabilitate aggressive and out of control dogs with alpha-rolling, waving open scissors around a dog’s face as it snaps at their hand (as Cesar Millan does in one video that I can’t find right now) and similar crap (and they can), then there’s no need for you to get started down the punishment-dominance-scare the dog into doing what you want road. If you are interested, the veterinary behaviorists have come out with a position statement - WARNING: PDF - opposing the use of punishment for training, spurred in part by the popularity of The Dog Whisperer. I’ll leave the rest for another thread (and there have been many).
Regardless of which school or theory of dog training you subscribe to, watching a TV show is NOT enough for the new dog owner. Even if you get an older dog, you should still attend obedience sessions with a competent trainer to make sure that you and your dog are on the same wavelength. You can ask your vet and/or the shelter/rescue for references. Before signing up for a class, go observe a class or two with the trainer you are thinking of. Do the dogs look happy to be there? How do they react to their owners and the trainer? They should be relaxed or exuberant, not scared or aggressive. Is the trainer friendly and good at explaining things to the people? They are really teaching YOU to train the dog.
Regarding what dog to get, it is possible to find out before you adopt whether the dog is good with cats. Ideally, you would go with a rescue group that places their dogs in foster homes to see how they react to being in a busy household with children, other animals, and busy schedules. A good rescue - or a well-run shelter - will interview you to determine your needs and then make recommendations of individual animals based on what they feel would be the best fit. Of course, there are rescue people who are nutters and rescues with unreasonable expectations, but there are good ones out there. Depending on the breed/size/individual dog, even adolescent or 1 year old might be on the young side. Some dogs/breeds tend to act like goofy puppies for a couple years before settling down (and then there are those who never settle down).
At least right now, the 5 y.o. and the dog should NOT be left together unsupervised. At some point later, when you know the dog better and the kid knows more about how to act around dogs, you can trust them together, but during the adjustment period, 5 is too young to trust that neither will hurt the other, even accidentally. E.g., kid is petting dog, dog gets sick of it (or is stressed for other reasons, including the new household), dog gives warning signs, kid doesn’t recognize warning signs and continues petting/pestering dog, dog nips kid. JMHO.