Is there any way to change the order of retainers without releasing or resetting?

I had five retainers at one point, but I'm trying to cut down to three

I'm using the last two to store items that I don't want lost but I don't need to access every month. Some old glamour or tokens that I don't want to dump.

The issue is, when I want to cut down to three, it has to specifically be the first three that I created.

Retainer #1 is my ex-main battle class
Retainer #2 is a MIN
Retainer #3 is a BTN
Retainer #4 is a FSH
Retainer #5 is my new main battle class

Looks like I only want three active retainers on my subscription, it has to be specifically 1-3
But I want 2, 3, and 5

But it looks like the only way I can have retainer #5 active while only having three retainers active is by releasing both retainers #1 and 4

I don't want to release any of them because I might need them at some point, and I'll have to re-level them to 60. But my goal here is to have my active retainers be 2, 3, and 5. If I could swap 5 and 1, I'd be happy. Is this possible?

I don't think there is this possibility now. For your situation, I'd suggest releveling your #1 to your current main, -or- leveling that old main class of yours he has to level 60. Since I don't know which classes are in question I can't say how feasible this is regarding hand down gear. But I think either of these two options is less hassle than releasing two retainers.