I have a friend who is to receive an under $5000 distribution from a qualified plan. Does anyone know how much time the former employer has to make that distribution to her?

Depends mostly on the plan provisions.
Many plans do not pay out until the employee has incurred a "break-in-service". (There are usual exceptions when the distribution is on account of death or disability or retirement.) A BIS is defined as a plan year in which the employee works 500 or fewer hours. After that BIS has been achieved, the plan might make distribution "as soon as administratively practical."

Example, assume the plan year is a calendar year, and EE severs employment on May 1, 2001. Most full-time employees will have worked about 650-700 hours in those 4 months. Therefore, this EE will not have a BIS until 12/31/2002, assuming not rehired.

EE should read the summary plan description to see what plan does in this case.