I'm not requesting additional services or additional transportation costs, so it really will not cost the district any more money.
Ah, but they are looking much further into the future than next year. Unless you already intend to keep him in school through age 21, he will be using an extra year of services/costs by repeating 5th grade. And if you do intend to keep him in school until 21, they may not feel there is reason to retain at this point as they'll continue working with him at his level regardless of which "grade" he's enrolled. I'm not saying any of that is adequate excuse for advancement, and they aren't legally allowed to use financial as a reason, but they most certainly are looking at it that way.
But the principal wouldn't have recommended it because he was never involved in any aspect of my son's education.
The principal is just the authority figure in such situations, the recommendation(s) likely come from your son's usual day-to-day teacher(s) or case manager. Or as more likely the case, his teachers haven't suggested retention, therefore by default the recommendation is advancement. Is there a district-level person you can appeal to? Here, I don't even attempt to deal with the school principal as any higher-up decisions are made by the district-wide Director of Special Education, who reports to the Superintendent.
Have they been working with your son on transition to 6th grade? Schools are so different that I can't tell from your post if that means a new school (different building) or a different classroom. If it's a big change and they know he struggles with change but they have not worked on transition, that should help support your request to retain. But I'd also make sure your request shows how retention will ultimately help your son -- will the extra year bring him closer to grade-level academically? What is the goal -- your goal -- with retention? If he is not performing at grade-level and isn't likely to catch-up to grade-level by repeating 5th grade, what are you hoping for him to gain? I honestly think with kids who fall so far behind their peers, and are on IEPs, advancement is less about the academic deficiencies and more about achieving the goals set forth in his IEP. If you can show they haven't been making forward progress towards those goals, you might have a stronger argument than test scores. And if he struggles with change, they really need to have transition goals written into his IEP to help him move to the next step (be that just the next grade, new building, different schedule, etc.).
Good luck!