  In this paper, we construct a family of elliptic curves with rank $\geq 5$.
To do this, we use the Heron formula for a triple $(A^2, B^2, C^2)$ which are
not necessarily the three sides of a triangle. It turns out that as parameters
of a family of elliptic curves, these three positive integers $A$, $B$, and
$C$, along with the extra parameter $D$ satisfy the quartic Diophantine
equation $A^4+D^4=2(B^4+D^4)$.
