People seem to like him, and people support him and the show already. There is no reason why the show wouldn't continue for at least five years as people in these positions have historically stayed in the positions for many years, even decades. He'll probably do well for a while.
Yes, Jimmy Fallon will likely be the host of the Tonight Show for a period of longer than five years. The two major previous hosts I can think of, Carson and Leno, both hosted the show for a substantially longer period than five years. Only Conan O'Brian hosted for a shorter time period. Plus, Jimmy Fallon is very funny and well-liked.
After reading some of the comments after his first night the only really negative comments were from people who had watch Johnny Carson. Humor has changed over the years, and I think Jimmy Fallon gives a sincere and refreshing energy to late night comedy. I do believe he will last 5 years, and I think he will last way longer than 5 years.
No, I do not think that Jimmy Fallon's tenure as host of the Tonight Show will be longer than 5 years, because he is already starting out with ratings that are not very good. People do not understand why Jay Leno was forced to leave, and that is making them skeptical of Fallon off the bat.
I don't think Jimmy Fallon's tenure as host of The Tonight Show will be longer than 5 years. I think Fallon's viewers are used to seeing him at 12:30 p.m. whereas Leno's viewers were used to seeing him at 11:30 p.m. These hosts appealed to different audiences of different ages, and I don't think this change will be that successful or long-lasting.