IPhone 5 Alarm sound question
Yes and no. The iPhone has a reasonably sophisticated, system-level, sound setup with the goal of making it easy for the user. It has several volume options divided up. (1) all alerts such as ringtones and Alarm.app alarms, (2) Siri, (3) content playback such as music or video.

Yes: What you can do to directly fix your problem is to use the vibrate/silence switch on the side of the phone instead of turning the ringer volume down. In the on position (orange is showing, a vibration is felt when the switch is initially turned on), phone calls, texts, and such will vibrate, but the alarm will still play at whatever the ringer volume was set to before turning the vibrate switch on.

One other thing you could do is leave the volume switch on and purchase, or create, a silent ringer - no music in it. Then you can select that ringer as your default ringer and calls will be "silenced". This method is generally not preferred because custom contact ringers will override this ringer.

No: The vibrate switch is actually the only way to separate the ringer volume from the alarm volume. If the vibrate switch is off (calls are heard), then the alarm volume will match the ringer volume.