<p>The weighted essentially non-oscillatory (WENO) scheme is a high-order numerical technique widely used for accurately approximating solutions that contain discontinuities. A crucial component in the construction of a WENO scheme is the formulation of nonlinear weights corresponding to each substencil. The primary challenge lies in substantially diminishing the contribution of substencils that contain discontinuities, while accurately retaining the linear weights in smooth regions. In this context, the present study proposes a novel strategy for constructing nonlinear weights in fifth-order WENO schemes. The key idea of our approach is to modify the unnormalized nonlinear weights in a way that amplifies the scale differences among them when a discontinuity exists within the global stencil. Accordingly, compared to existing fifth-order methods, the proposed technique exhibits an enhanced capability to distinguish non-smooth substencils from the smooth ones. In addition, we verify that the resulting WENO scheme maintains fifth-order accuracy, even in the presence of critical points. Several numerical results are provided to demonstrate the improved performance of the suggested WENO method.</p>