(CNN) The race for control of the Senate is exceedingly close -- so much so that there's a distinct possibility of a split chamber for the first time since 2001.

Democrats need four pick-ups to win the Senate if Hillary Clinton wins the White House -- five seats if Donald Trump wins since the vice president breaks the tie. There are three GOP seats that Democrats now have a clear edge in winning, while five seats are still toss-ups.

Republican presidential nominee Donald Trump remains the biggest wild card affecting control of the next Senate majority. If he can keep his margin close with Hillary Clinton, within two to four points, it will help Republicans down-ticket immensely, according to party leaders. But if he continues to slide, the GOP chances of losing the majority grow remarkably.

That's one reason why Republicans are struggling to deal with the Trump factor: They want to distance themselves from his inflammatory comments, but they need him to do well in their states.

But at the same time, Clinton's lingering unpopularity limits how long her coattails will be down-ticket.

Five weeks out from Election Day, here is CNN's list of the seats in order of most likely to switch hands -- based on public polling and interviews with top officials in both parties.

Seats most likely to flip

Republican-held seat in Wisconsin

This is a peculiar race in which the challenger, former Sen. Russ Feingold, is better known than its incumbent, first-term Republican Sen. Ron Johnson. Polls have consistently shown Johnson down between six to 10 points, and his challenge is made even harder because the difficulties Republicans have in the state during a presidential election year. The Johnson campaign believes the race is much tighter than public polling shows. LIKELY DEMOCRATIC WIN.

Republican-held seat in Illinois

This deep blue state makes it very difficult for Republican Sen. Mark Kirk to hold, facing off against Rep. Tammy Duckworth, an Iraq war veteran. But even as Kirk has been written off for much of the year, he is only down between two and five points, depending on the poll. And with presidential candidates not competing in Illinois, it gives Kirk an outside chance, especially as he separates himself from Trump. But a new poll out this week from Southern Illinois University shows Duckworth holding a commanding 14-point lead, something Kirk hopes is an outlier. LIKELY DEMOCRATIC WIN.

Republican-held seat in Indiana

Former Sen. Evan Bayh's late entrance into the race gave the Democrats a candidate with a well-known family name and a load of campaign cash to compete against a little-known GOP congressman, Todd Young. But Bayh has struggled to overcome questions about his post-Senate life and whether he abandoned the state to enjoy the luxuries of Washington. His lead, which was double digits initially, has now narrowed between four and seven points. Democrats have the advantage, but Republicans are still bullish here. LEANS DEMOCRATIC.

Republican-held seat in North Carolina

Republicans are panicking about North Carolina, worrying that Trump's controversial candidacy, passions in the state over the so-called "bathroom bill" pushed by conservative state lawmakers and an unpopular Republican governor will amount to a perfect storm -- and cause Sen. Richard Burr to lose against a little-known opponent, Deborah Ross. Republican money is beginning to flood into the state to help save Burr, who has been criticized for not aggressively campaigning.

But Ross has been raising millions of dollars and has the full backing of the party establishment. And both candidates are aligning themselves with their party's nominee. Recent polls show Ross winning the race, putting a scare into the GOP, and a Quinnipac University poll released Wednesday says the race is tied. TOSS UP.

Democratic-held seat in Nevada

Senate Minority Leader Harry Reid's legacy is on the line in this state. Yet his hand-picked successor, Catherine Cortez Masto, has had trouble overcoming the lead of Rep. Joe Heck, a congressman from a populous district in Southern Nevada who has gone to war with Reid for years. Heck has made the calculation to mostly align himself with Trump, distancing himself sparingly from the GOP nominee, and it appears to be paying off for now, as Trump is neck-and-neck with Clinton in the polls there. Reid is going all-out to defeat Heck and is unleashing his political machine in the state to defeat him. TOSS UP.

Republican seat in Pennsylvania

Pat Toomey, the GOP incumbent, is in a bind when it comes to Donald Trump. The Republican nominee, who won the state big in the primary, is competing aggressively to win in the general election.

Toomey, who hasn't hidden his disdain for Trump and hasn't fully endorsed him, is in a tough spot. He needs Trump's voters but at the same time is seeking to win over voters in the Philadelphia suburbs -- including women who have been put off by the GOP nominee's rhetoric.

He's battling Democrat Katie McGinty, who is narrowly leading in most polls but within the margin of error. The new Quinnipiac poll shows Toomey up 50-42 in the state, but officials in both parties believe it's a neck-and-neck race based on other public polling. TOSS UP.

Republican seat in Missouri

Sen. Roy Blunt, the veteran Republican, was supposed to skate to reelection. But he has found himself suddenly in a race that's too close too call because an attractive young Democrat, Jason Kander, has used Blunt's incumbency and long-standing ties to Washington against him. Kander's insurgent candidacy has put Blunt and the GOP on the defensive, as both sides are now dropping millions into this red state. TOSS UP.

Republican seat in New Hampshire

Republican Kelly Ayotte, the New Hampshire senator, has had to navigate the Trump terrain, saying awkwardly that she supports him but doesn't endorse him. At a Monday night debate, Ayotte was forced to clean up her remarks that she "absolutely" sees Trump as a role model. But her opponent, Gov. Maggie Hassan, has been attacked for being too scripted, and also has to contend with a Democratic standard-bearer who is distrusted in the state, something she has struggled with answering in the past. The national dynamics will play in heavily here, something that could put Ayotte in a bind if Trump's numbers continue to fall. TOSS UP.

The rest of the seats are being monitored by both sides but unlikely to flip -- as of now

Ohio seat held by Sen. Rob Portman (R)

Florida seat held by Sen. Marco Rubio (R) (Wednesday's Quinnipiac poll showed Rubio up by just 4 points against Rep. Patrick Murphy, a tighter margin than other surveys.)

Arizona seat held by Sen. John McCain (R)

Iowa seat held by Chuck Grassley (R)