Can my wife get life insurance behind my back, even after we have been separated for 5 years?

Insurable interest refers to the right of property to be insured. It may also mean the interest of a beneficiary of a life insurance policy to prove need for the proceeds, called the "insurable interest doctrine". Specifically, insurable interest is:

• An interest based upon a reasonable expectation of pecuniary advantage through the continued life, health and bodily safety of another person, and, consequently, loss by reason of their death or disability; or
• A substantial interest engendered by love and affection if closely related by blood or by law.
  —Society of Actuaries

Insurable interest is no longer strictly an element of life insurance contracts under modern law. Exceptions include viatication agreements and charitable donations.

has an insurable interest in the life of that second person.

Legal guidelines have been established in many jurisdictions which establish the kinds of family relationships for which an insurable interest exists. The insurable interest of family members is assumed to be emotional as well as financial. The law allows insurable interest on the presumption that a personal connection makes the family member more valuable alive than dead. Thus, husbands/wives have an insurable interest in their spouse, and children have an insurable interest in their parents (and vice-versa). Brothers/sisters and grandchildren/grandparents are also assumed to have an insurable interest in the lives of those relatives. But cousins, nieces/nephews, aunts/uncles, stepchildren/stepparents and in-laws cannot buy insurance on the lives of others related by these connections.

Answer: So long as you are not divorced, your separated wife can place a life insurance policy upon your life.