5.After lengthy discussion, it was decided the patient would continue to be treated in the hospital.

Is there any conjuction in this sentence.

No.

There is one SUBORDINATING conjunction in this sentence:

http://grammar.ccc.commnet.edu/grammar/conjunctions.htm#subordinating_conjunctions

What do you think?

Isn't after a preposition in this sentence?

Yes, it's "after."

Yes, there is a conjunction in this sentence. The conjunction is "but" which connects two clauses: "After lengthy discussion" and "it was decided the patient would continue to be treated in the hospital." The use of the conjunction "but" indicates a contrast or opposition between the two clauses.