There is one closet and 5 drawers, all full of clothes. We had to buy a clothes rack because there wasn't enough room for all her clothes. She keeps asking us to buy more clothes and there is not enough room, I hate to be mean and say no, but we cannot fit any more things in her room.
You will now have to accept the responsibility to make her decisions for her.
"Mom, you have limited space, and don't need more clothes, so we aren't going to buy more for you unless there is an outfit you wish us to put in a donation bin somewhere. Love you, but you cannot clutter the room with these things".
Sweet smile. Move on.
If this is a bit of a compulsion, then you are dealing with a bit of a compulsion.
But in any case, there's nothing mean here at all.
Really, you should never have brought in a rack. My Mom had nine outfits. More than enough for the laundry turn around. I put tops with matching pants. Later even her bra, long story. I only had her seasonal clothing there. Her others were in a tote in my spare bedroom.
Realize your mother is stuck in a loop thinking pattern which goes with dementia, saying she needs more clothing when she obviously does not. It's not "mean" to use techniques to distract her from thinking she needs new clothing all the time. It's helping her to have room to breathe in a tight space!
So, to help with your dilemma, I go along with the others, with a little more specifics. Go back to all her clothes being in drawers or in a closet. Then cycle them in/out. Keep the ones that she uses constantly in her room, however, cycle in/out the others.
See if you can find out why she is requesting more clothes. Is it because there are specific colors or patterns are not present? Is it because she expects her room to be cramped full of clothes and it isn't? Is she looking for specific articles of clothing and it isn't there (e.g. looking for bulky sweaters in the summer). It could be that all she wants is a clothes shopping trip (not to try on or buy, but to smell and feel the texture and the newness). Or maybe you need to wash some of her clothes with a different laundry detergent to get a varied smell to her wardrobe.
Instead of pointing out that she already has lots of clothes, ask her why does she want more clothes. Also ask, what kind of clothes does she want and why.
Good luck!