Could it be syphilis?

Jack, a 52-year-old sales agent, presents with a disseminated rash for over two weeks.
The rash is reddish, not painful or itchy, and a little raised.
It involves the face, trunk, abdomen, arms, legs, palms and soles. Jack has also had fever, headache, lethargy and myalgia for over two weeks.
He is an ex-smoker who drinks alcohol occasionally. Jack has no significant past medical history, though is allergic to penicillin.