Step 1 :The given equation is in the form of an exponential equation, where the base is 'w', the exponent is '-5' and the result is 'r'.
Step 2 :The equivalent logarithmic equation would be in the form of log_base(result) = exponent.
Step 3 :So, we need to substitute 'w' as the base, 'r' as the result and '-5' as the exponent in the logarithmic equation.
Step 4 :The equivalent logarithmic equation is \( \boxed{\log _{w}(r)=-5} \).