In some enzyme$-$catalyzed reactions, multiple complexes are involved as follows:

$E+S{}^{k_1}{?}^{k_2}ES$

$(ES{)}_1{}_{k_4}^{k_3}(ES{)}_2$

$(ES{)}_2{}^{k_5}E+P$

Develop a rate expression using

$($a$)$ the Michaelis$-$Menten approach and

$($b$)$ the Briggs$-$Haldane approach.