(NO) Two intersecting lines cannot be both perpendicular to the same line because if two lines $l$ and $m$ are perpendicular to the same line $n$,then $l$ and $m$ must be parallel to each other.
Euclid's fifth postulate states that if a line segment falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles,then the two straight lines,if produced indefinitely,meet on that side on which the sum of angles is less than two right angles.
Since the given statement describes the property of parallel lines and not the intersection of lines based on interior angles,it is not an equivalent version of Euclid's fifth postulate.