I found this discussion by searching the web. My wife and I have identical iPhone 5 phones. The volume of the dial tones on her phone when entering a phone number is much lower than on mine. After searching the web, this appears to be a generally recognized problem. None of the settings appear to affect the volume of the dial tones. and the only solution is to entirely mute the phone with the side switch, a very unsatisfactory answer. I am surprised that Apple or a third-party developer has not addressed this.
One solution that was provided by an Apple tech in a post on another website was to do a soft reset by pushing the power butter and the main button on the front at the same time until the Apple logo appeared. I tried this and the dial tone volume was lowered to the same level as on my wife's phone.