Will increasing a COPD patient's oxygen when taken to 5, 000 ft altitude injure her?

Usually not. Check with the doctor to make sure the patient does not have a tendency to retain carbon dioxide. Also, it is best to have an oximeter, a device that measures oxygen levels, with you. It will allow you to use just enough, not more not less.
Yes and no. At 5, 000 ft altitude, everyone needs more oxygen than at sea level. So a COPD pt will need a corresponding increase in her oxygen. That should not be injurious as long as it is coordinated with a physician. Where is she going? Outside of the us, this will very unlikely be feasible.