Let's consider how this might work out in a recent year. Let's take 2022, since the Vols did so well that season.
First, who were the five highest-ranked conference champs (because they would all be guaranteed a playoff spot)?
#1 Georgia was the SEC champ
#2 Michigan won the B10
#7 Clemson was ACC champion
#8 Utah was the PAC's leader
#9 Kansas State won the B12
The first four of those would have been slotted for first round byes, so would start like this:
1-seed - #1 Georgia
2-seed - #2 Michigan
3-seed - #7 Clemson
4-seed - #8 Utah
Oh, and one other team would be guaranteed a spot in the playoffs, as well--the highest-ranked G5 team. That would be #16 Tulane.
So 6 spots taken, the rest would be given, in order, to the highest ranking remaining teams.
5-seed - #3 TCU
6-seed - #4 Ohio State
7-seed - #5 Alabama
8-seed - #6 Tennessee
9-seed - #9 Kansas State
10-seed - #10 USCw
11-seed - #11 Penn State
12-seed - #16 Tulane
Now, let's follow a few teams through the brackets, to get a feel for who might have the easier road. Of course, we'll follow the 5-seed, that's what this thread is about. But let's also follow the 1-seed, the 4-seed, and the Vols (6-seed).
5-seed: #3 TCU would have been the 5-seed. Remember, they were the cinderella team of that season--picked to lose game after game, they just kept winning, until losing to Kansas State in the B12 championship game. Nonetheless, the CFP Committee put them in the playoffs.
In this alternate world with a 2022 12-team playoff, TCU would've faced #16 Tulane in the first round. If they'd won, in the next round they would take on #8 Utah. Then, in the semi-finals, they'd get #1 UGa (or #6 Tennessee), then finally if they kept winning, #2 Michigan (or someone who beat Michigan). Their sequence of opponents: #16, #8, #1, #2 at highest.
8-seed: the Vols, by comparison, would have this sequence: home game in the first round against #9 Kansas State ... then #3 TCU ... then #1 UGa .... finishing off with #2 Michigan. Sequence: #9, #3, #1, #2. Significantly harder than the 5-seed's path.
4-seed: #8 Utah would start with a bye ... then face #3 TCU ... then #1 UGa ... and then #2 Michigan. That's a rough route: bye, #3, #1, #2. Allowing for the bye, it would otherwise be just as hard as the 8-seed path.
Finally, let's follow:
1-seed UGa: in the first round, they would have a bye ... then #6 Tennessee ... then #8 Utah ... and finally 2-seed #2 Michigan. Their sequence: bye, #6, #8, #2.
Easiest path: starting in the 1-seed spot. Of course.
But as the OP pointed out, the 5-seed path would be pretty sweet, too. Certainly better than the 4-seed or 8-seed.
Go Vols!