We construct a new infinite family of pairs of imaginary quadratic fields with both class numbers divisible by five. Let n be a positive integer that satisfy n 3 (mod 500) and n not equivalent to 0 (mod 3). We prove that 5 divides the class numbers of both Q(root 2 - F-n) and Q(root 5(2 - F-n)) where Fn, is the nth Fibonacci number. (C) 2017 Elsevier Inc. All rights reserved.