$(1+1+1+1+1=5$ points$)$ Consider the statement $5<2<3.$

$($a$)$ Use P and Q to write this statement formally.

$($b$)$ What is the value of this statement?

$($c$)$ Write the negation of this statement formally $($in P and Q$).$

$($d$)$ Write this negation in plain English.

$($e$)$ What is the value of the negation?