The latest rumors appear absurd because Frank Underwood is suffering from an ailment so having the presidency and dealing with his illness would mean that his plate is full for the upcoming Season 5.
It is possible that the rumors of Frank getting a new love interest in the upcoming fifth season of “House of Cards” were spawned by the fact that he and Claire have already parted ways as a couple back in Season 4.
They may not have to agree on a lot of personal things but when Frank was re-elected President of the United States and Claire as his Vice President, they have no other recourse but to work together for the good of the country and the American people.
The same rumors are saying that Frank getting a new lover could be the impetus for Claire to plot the murder of her husband and take over the presidency of the country.
Also in the same mix of rumors, Claire shall apparently use Doug Stamper, the most trusted and loyal ally of Frank, as her hit man in liquidating the President.
However, all these are mere speculations pending the confirmation or denial from the showrunner, the cast members, or Netflix, which is unlikely to happen anytime soon.