Marginal utility of x = du/dx = 5 (y/x)^{1/2 (1)}

Marginal utility of y = du/dy = 5(x/y)^{1/2 (2)}

Marginal rate of substitution (dividing 1 by 2) = dy/dx = y/x

This marginal rate of substitution declines with an increase in x. Therefore, it is diminishing with an increase in x.