Solution
= Solution
The axis intercepts of the <plane> are
$$
P=(-5,0,0),\qquad Q=(0,5/4,0),\qquad R=(0,0,5).
$$
Use two edge <vectors> from $P$:
$$
(Q-P)\times(R-P)
=(5,5/4,0)\times(5,0,5)=(25/4,-25,-25/4).
$$
The <triangle> area is half this <cross product> magnitude:
$$
\boxed{\mathcal A=\frac12\frac{25}{4}\sqrt{1+16+1}
=\frac{75\sqrt2}{8}.}
$$