If the drive belt snapped you would have lost power steering also and most likely wouldn't have been able to drive further. In order to check charging you need to jump start the X5, hook up a voltmeter to the connection points in the engine bay (one under the red plastic cover the other to the body). The voltage should be in the 13.7-14.7 range but typically around 14.0 volts.
If it does not charge even with a brand new or newly charged battery you won't make it far.