The term 'PET PROBLEM' can be broken down into two crossword solutions: PEEVE (5 letters) and LICE (4 letters). PEEVE is a noun that means a feeling of annoyance or irritation caused by something trivial, unreasonable, or impossible to control. LICE are small, wingless insects that live on the skin of mammals and birds and feed on their blood. Both PEEVE and LICE can be considered pet problems, as they can cause discomfort and distress to animals.