The Toffees have never lost to the Welsh outfit in any competitive meeting, winning 13 and drawing five of their 18 clashes.
That includes a 2-1 win at the Liberty Stadium in late December, thanks to Ross Barkley's exquisite late free-kick.
If Everton advance, the final eight will involve just two sides above them in the Premier League.
Roberto Martinez can pick from a rested squad after Wednesday's game with Crystal Palace was postponed.
The exact same personnel are available to the Catalan, as he revealed during his pre-match press conference, via Everton's official website:
We are exactly the same as we were on Wednesday in terms of numbers. We have the same squad, with the three long-term absentees.
Those long-term injuries are Bryan Oviedo, Darron Gibson and Arouna Kone, while Romelu Lukaku and Antolin Alcaraz will also miss out.
The extra time off gives the likes of Lacina Traore and Gerard Deulofeu—both short of match fitness—a chance to do additional work on the training ground, as Martinez also revealed:
RM: "Lacina is getting there and he's working really hard. He's benefitted from having these extra couple of days." http://t.co/V1KosZbym0— Everton (@Everton) February 14, 2014
With that team news considered, here's a look at Martinez's potential starting XI:
Prior to this fixture, Everton's FA Cup lineups have had something of a rotated look about them.
However, following the inviting fifth-round draw, expect Martinez to prioritise this competition a little more.
Which player not in this XI should start?
That should mean a return in goal for Tim Howard, who is yet to feature in any cup game this season.
Everton's first-choice back four will play for only the third time in 16 games, as will the key partnership of Gareth Barry and James McCarthy just in front of them.
As always this season, it's the four attacking berths that will be most deliberated over.
Kevin Mirallas was surprisingly omitted from the lineup to face Palace, presumably rested for this game. The Belgium international is the most likely starter out of Everton's batch of attackers.
Steven Naismith will give more presence up front than any other option and, given their lack of action this year, Traore and Deulofeu are more likely to start on the bench.
That leaves Barkley, Leon Osman, Steven Pienaar and Aiden McGeady fighting over the remaining two berths.
There's certainly an argument to start McGeady and Barkley, the more direct of the four choices.
However, Barkley's yet to appear fully fit since his return, and Martinez may prefer the guile and ingenuity of the more experienced pair, at least to start with.
Swansea are one of only seven sides to have recorded more possession against the Toffees this season. In fact, only Southampton and Chelsea have managed a higher proportion to the Swans' 55 percent.
Who makes the final eight?
Therefore, the battle and retention of possession will be key to both sides enforcing their desired approach.
Barry and McCarthy will be tasked with winning this contest against Swansea's deep midfielders, presumably Jonathan De Guzman and Leon Britton.
At the same time, with one side committing bodies forward, turnovers will also be pivotal. Mirallas' pace will be important for Everton, as will the direct play of Barkley and Deulofeu, if and when they are introduced. Bringing on pace with half-an-hour to go may play an important role.
Barkley was particularly prominent bursting forward during December's clash, making more successful dribbles than any other player.
Prediction: Everton 2-1 Swansea
Statistics via WhoScored.com