Deciding an order is not picking one name five times. It is drawing the whole line at once.
Presentation order, whose turn it is in a board game, the cleaning rota. Ask "who wants to go first?" and nobody moves. So you pick at random — and depending on how you do it, there is grumbling afterwards or there is not.
The usual way is to spin a wheel for first place, remove that name, spin again for second, and so on. The odds are fine. But six people means five spins, and five chances for "that spin didn't count, my finger slipped".
Setting an order is really drawing the whole line in one go. One draw leaves no room for re-spins, and everyone watches the same thing once.
Race Roulette draws the full ranking of every participant at once, then plays a race in which the runners cross the line in exactly that order. First to last is your order.
With a lot of people a race takes longer; use 2× or 4× speed, or set laps to 1. Nothing is saved, so screenshot the results board if you need to keep it.
If someone went first last week and you want them less likely to go first again, give them fewer boosters (a lower weight) than everyone else. The lower the weight, the lower the chance of finishing near the front. Boosters are shown on screen, so everyone can see who got what.
A weight of 0 means they effectively never win. Unless you want them out, use small differences like 1 and 2 instead.
A race holds up to twelve, so for a whole class you split into groups first. How to split fairly and how to draw several times without repeats is in when you need more than one pick.