There are plausible ways for Genesis 1-5 to be a combination of figurative, cultural accommodation, and literal, including a literal Adam and Eve, without contradicting science.
Major Christian Approaches to Creation:

1. Young-earth Creation (YEC)
Promotes a literalistic biblical interpretation of Genesis with a six-day creation approximately 6,000 years ago.

  • Theological Tradition: Fundamental (& a sizable portion of Evangelical), particular after the reformation and especially with the rise of fundamentalism in the 20th century.
  • Genesis Interpretation: Literalistic and based on modern understanding of scripture. Believes that the author, hearers/readers would have understood in a similar way that we do.
  • Science Compatibility: YEC denies a 14 billion year “old” earth & universe, and evolution. It is not accepted by at least 98% of mainstream scientists.[1]
  • Leading person & group: Ken Ham www.AnswersinGenesis.org
  • Video and More info: The Case for Youth-Earth Creation

2. Old-Earth Creation (OEC)
Accepts mainstream science on the age of the universe and the earth, but not on evolution.

  • Theological Tradition: A sizable portion of Mainline Protestant denominations and a significant portion of Evangelicals. It arose in the late 20th century in reaction to extensive evidence of a much older earth and universe than YEC allowed for.
  • Genesis Interpretation: Says Hebrew word, “yom” could be translated as “eras” instead of 24 hour days. Otherwise, generally accepts a literalistic interpretation of Genesis, except in the case of the flood believes the interpretation of Hebrew word “erets” probably referred to a regional flood.
  • Science Compatibility: OEC accepts Big Bang, a 13.7 billion-year-old Universe, and 4.7 billion-year-old earth, but denies the mainstream scientific view (98% [1]) of evolution and also DNA evidence that there were at least 1,000 individuals in the initial group of modern humans instead of 2.
  • Leading person & group: Dr. Hugh Ross: Reasons to Believe (www.Reasons.org)
  • Video and More info: The Case for Old-Earth Creation

3. Evolutionary Creation (EC) (aka Theistic evolution - TE)
Accepts mainstream science on the age of the Universe & Earth but believes that God created humans through evolution. It does not have a designated view of Adam & Eve, but has various plausible scenarios.

  • Theological Tradition: Unknown prior to Reformation. Since the beginning of 21st century, a sizable portion of Catholics, Mainline Protestant denominations, and small but growing numbers of Evangelicals.
  • Genesis Interpretation: It views early Genesis stories as at least partially figurative. It does not espouse a single theory on Adam & Eve but has multiple scenarios (see link below).
  • Science Compatibility: EC is compatible with mainstream science.
  • Leading person and group: Dr. Francis Collins: www.BioLogos.org
  • Video and More info: The Case for Evolutionary Creation.

4. Intelligent Design (ID)
A limited theory that believes in a designer without identifying the designer. Adherents of this view can be YEC, OEC, and occasionally EC or those who are non-committal on creation theories. Can believe in evolution, but has scientific-like arguments against non-miraculous evolution.

  • Theological Tradition: Is not directly connected with the belief in a Christian God, although many adherents are Christian. It began in the late 20th century.
  • Mainstream Science Compatibility: Because of controversial and scientifically refuted stands, ID has been rejected by the world largest scientific society, the American Association for the Advancement of Science.[3] However, since there are a variety of ID arguments, some may be very logical, but still hard to prove.
  • Leading person and group: Michael Behe: Discovery Institute (www.discovery.org/id/)
  • Video and More info: The Case for Intelligent Design.

 

For More Information:

Christian Views on Adam & Eve - a table of 6 different views.

Wikipedia info on Evolution-Creation Controversy

1. A PewInternetResearch.org, January, 2015 Survey among AAAS (American Association for the Advancement of Science) shows scientists and others in scientific fields shows 98% believe in a very old earth/universe and evolution" [http://www.pewinternet.org/files/2015/07/AAAS-Members-Elaboration-7-16-15-FINAL-Appendix-A.pdf]. This does not mean that they reject all faith approaches. 33% believe in God and 30% are Protestant or Catholic [http://www.pewforum.org/2009/11/05/scientists-and-belief/]

2. [http://archives.aaas.org/docs/resolutions.php?doc_id=432]