Determine the value of '$r$ ' for which the equation $13x+5=rx+18$ has no solution.

A linear equation in the form $Ax+B=Cx+D$ has no solution if the coefficients of $x$ on both sides are equal, but the constant terms are different.Rearranging the given equation:
$$(13-r)x=18-5$$
$$(13-r)x=13$$
For this equation to have no solution, the coefficient of $x$ must be equal to $0$, so that the left side becomes $0$ while the right side is a non-zero constant ($13$).
$$13-r=0⟹r=13$$