本を読んでいたら。- I just do not understand this grammar.

本を読んでいたら、いつの間にか五時間も経ってしまった。

I have always hated たら when used in the sense of WHEN rather than IF, but this one is killing me.

Why in this sentence can I not use 本を読んだら ?
what purpose does te PLUS tara serve?

I understand たら well in sentences like this;

ご飯を食べたら、寝ます
朝起きたら、歯を磨きます。
店に行ったら、デイビッドに会いました。

so where does the te form and たら fit in?

In my example, why is 読んだら not used?

Thanks again.

Five hours passed unnoticed WHILE reading the book (because it was so interesting); the reading and time passing were concurrent, not sequential.

When the verb expresses "state" in the たら conditional clause, the main clause is an event "while/during" it, as Mike-san explained. That's the reason 読んでいる is used there. The moment five hours passed was sometime while the writer was reading a book, not after they read it (= 本を読んだら).
e.g.
ご飯を食べていたら、眠くなりました。
"The moment I got sleepy" was sometime in "while I was eating". Note that ご飯を食べたら、眠くなりました。 means "I got sleepy after I ate meals" since 食べる is an action, not a state, unlike 食べている.

店にいたら、デイビッドが来ました。
"The moment David came to the shop" was sometime in "while I was in the shop".

Thanks for the answers guys.