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D = P + 5, (1) ("Don is 5 years older than Peter is")
D + 5 = 2*P (2) ("In 5 years, Don will be twice as old as Peter is now.")
From (1), substitute D = P+5 into equation (2). You will get
(P+5) + 5 = 2*P ====> P = 10.
Answer. Peter is 10 years old. Don is 10+5 = 15 years old.