Who are the top 5 linguists (by number of languages spoken) in all of
history?  What languages did the top two speak?

Richard Burton, the Explorer not the Actor, was reputedly one of the
best but I don't have a list.

"Mithridates VI of Pontus... was supposed to have had a prodigious
memory. He could speak twenty-five languages, and to be able to
address each soldier in his large armies by name, and in his own
tongue. This legend is alluded to in the short story Funes the
Memorious by Jorge Luis Borges.

From this legend, several books that published samples of many
languages were entitled Mithridates."

http://www.answers.com/topic/mithridates-vi-of-pontus

Here is a good candidate for your top five.

http://www.mezzofanti.org/mezzofanti.html
Giuseppe Caspar Cardinal Mezzofanti

Although specific estimates vary, historians generally agree that
Cardinal Mezzofanti spoke around 38 languages and 50 dialects
fluently, and spoke many other languages with less fluency. With this
amazing ability in language learning, Mezzofanti holds the world
record for multi-lingual fluency, and is considered the greatest
polyglot in history.