Stem Cell Research Enhancement Act of 2005 - Amends the Public Health Service Act to require the Secretary of Health and Human Services to conduct and support research that utilizes human embryonic stem cells, regardless of the date on which the stem cells were derived from a human embryo. Limits such research to stem cells that meet the following ethical requirements: (1) the stem cells were derived from human embryos donated from in vitro fertilization clinics for the purpose of fertility treatment and were in excess of the needs of the individuals seeking such treatment; (2) the embryos would never be implanted in a woman and would otherwise be discarded; and (3) such individuals donate the embryos with written informed consent and receive no financial or other inducements.