No. Apple won't be able to as the phone is with Sprint and you had to sign up for a 2 year contract with them when you purchased your iPhone 5.
If you want to try and get your phone unlocked, then you'll need to contact Sprint directly about it.
Also, remember that the warranty on the phone is only valid in the US, so any problems with the phone in Vietnam and it will have to come back to the US for fixing. Also, won't work with 4G and LTE due to differing frequencies between countries.
Have to say that Sprint probably will not unlock your phone for you, but you'll have to contact them to see and all in all it is not a good idea to plan to do what you are doing. Wait until the iPhone 5 is available through outlets in Vietnam and purchase one for you mother there.