National Board-Certified Teachers in Low-Performing Schools Act of 2005 - Directs the Secretary of Education to establish a pilot program of stipends for teachers in low-income, low-performing schools who: (1) are certified by the National Board for Professional Teaching Standards; and (2) serve as resident facilitators at their schools and as liaisons with the Board to help encourage other teachers to become Board-certified. Authorizes base stipends and potential bonuses for up to 100 teachers annually under such five-year program.