"My boss wants this report immediately. He demanded that it be ready by 5:00." "Should" is unnecessary and clutters the sentence, making it less clear.

Bassam, There is nothing wrong with the sentence. You must be taking a test using American English grammar rules. He demanded that it should be ready by 5:00. The sentence with should is common for British English--in order to avoid the subjunctive. Americans prefer the present subjunctive in a "that" clause after the verb "to demand". Subjunctive Present of "to be" I be You be He/She/It be We be You be They be In a typical British grammar, "English in Use" by Murphy for example, students are taught that both "should" and the present subjunctive are acceptable after verbs such as, demand, insist, etc.

Aaaaa! Aaaaaaaaaa! Americans are attacking the Holy British Grammar! Aaaaaaaaaa! My teacher would kill you, Daniel! :p

I agree with Daniel.

I'm not sure, but I think there is something wrong with the tenses... My boss wants this report immediately. He demanded that it should have been ready by 5:00. OR: My boss wants this report immediately. He demands that it should be ready by 5:00.