WILL THUMBS UP$!!!$ PLEASE help solve problems $5-10$ in a Carnap Proof Builder method $.$

$5.([$P $$ Q$]$ & Q$),($R $$ P$)([$P $$ Q$]$ & R$)$

$6.([$P & R$]->$S$),($P & $[$S $$ T$]),($R $$ P$)([$S & R$]$ T$)$

$7.($P $->$ R$)([$P & Q$]->[$Q & R$])$

$8.($P $->[$R & Q$])([$P & Q$]->$ R$)$

$9.($P $->$ R$),($Q $$ R$)($P $->[$Q & R$])$

$10.([$P & P$]->[$Q $->$ P$])$