Will my facial structure change if I have five missing back teeth?

Yes. When posterior teeth are extracted the cheeks can have a sunken in appearance. Many years ago, some fashion models foolishly had molar extractions to achieve this look.
Yes, over time. Once teeth that used to be there are no longer there, the bone that supports and holds the teeth in your jaw will start to remodel and resorb away. Osteoclasts slowly eat away the bone since there is no reason for the bone to stay there. As a result, your jaw will become thinner in that area and your face may have a shrunken in look. This process takes months to years for it to become noticeable.
Maybe. Loss of the larger back teeth will increase chewing forces and wear on the other teeth and cause eventual collapse of the bite. In time this could be reflected in your facial structure. Even though they don't show, the back molar teeth are crucial for proper chewing and digestion. Try to keep them if possible.