Statement 1 => |y|/|x| = -5 => x and y are of opposite signs => xy<0. Sufficient.
Statement 2 => |x|/|y| = -5 => x and y are of opposite signs => xy<0. Sufficient.
D as well,
but think about it -
(1) 5|x| + |y| = 0
When is a sum equal to zero? one is negative, one is positive. But || (absolute value?, not sure what is the English for it) can't be negative, thus both |x| an |y| should be equal to zero. This means xy clearly is not < 0, but equal to zero. Sufficient
(2) same thing for this option