I would not leave if I were her. However, if someone has a permanent residence status, they can be outside the country for 6 months maximum. 5 months would be too close for comfort in my opinion. I would not go until after I received citizenship. This response does not consitute an attorney client relationship. You may call me anytime at 206-613-3111 or e-mail me at email@example.com if you wish to have a free consutlation.
You (or she) can check the Guide to Naturalization for the eligibility requirements for naturalization.
The Guide is available for free at: http://www.uscis.gov/natzguide .
A naturalization applicant must maintain eligibility until after the oath ceremony.
One requirement is that the applicant must be physically present in the US at least a total of a number of days. If your mother has been travelling outside the US a lot, a trip of 5 months may push her over the allowable absence from the US.
Another requirement is that the naturalization applicant cannot be absent from the US more than 180 days at one time. Things have a way of coming up. If the mother is outside the US for 5 months, perhaps something will come up (such as getting sick, bad storm that delays travel) and push her stay over 6 months. Then, she has to wait 5 more years.
While the naturalization process does take a long time for some people, for most people it would take less than a year. If your mother is outside the US, she likely will not be able to respond in time to an appointment for fingerprinting or an oath ceremony.