  In this paper we illustrate the use of the results from [1] proving that
$D(4)$-triple $\{a, b, c\}$ with $a < b < a + 57\sqrt{a}$ has a unique
extension to a quadruple with a larger element. This furthermore implies that
$D(4)$-pair $\{a, b\}$ cannot be extended to a quintuple if $a < b < a +
57\sqrt{a}$.
