Dear Syed Ijlal Hussain,
To answer your questions, remember the difference between 'Muslim' and 'Momin'. 'Muslim' is a citizen of the state. He/she has decided to live under Islamic law, irrespective of his religious faith. With time, as he/she sees the benefit of living in the Divine Order, he/she will become more convinced of its truth.
Before Islam, the various tribes of different faiths were at war. The Rasool helped them unite under one law. The tribe members of different faiths benefitted from the Divine Order. Some of them changed internally and became momineen. Others did not, and remained as Christians and Jews, even though they were otherwise good citizens of the state. That's when the question of marrying these people must have originally arisen.
1) If we conclude that All Christians and all Jews are Mushriks, then why the need for Verse 5:5? Furthermore, why does The Quran refer The Christians and The Jews as people of the book, and not as the run of the mill Mushriks?
I would say they are called People of the Book because their ancestors received the Book, but this is in no way a comment on their present psychological state. Most were practising mushrikeen in their private religious lives. So they were 'Muslim' (citizens of the Islamic state who were involved in salaat and zakaat but had not yet 'believed' - see 49:14-15) but the internal change was taking longer. So, they were 'part-time' and not 'run-of-the-mill' mushrikeen. :) Note that in 5:5 the Quran is telling momineen men that they should marry those Christians and Jews who have formally changed internally.
2) Another question arises: What are the Muslims divided into sects to be called? Muslims or People of the Book?
Muslims divided into sects are mushrikeen. Difficult to say, but true. As I see it, the verses in the Quran address momineen living in an Islamic state alongside People of the Book.