Temperature doesn't necessarily equate with lumens. I prefer closer to 2700K (warm), as once you pass 3000-5000 it's just a very harsh white, but a higher number of lumens (depending on space 1500+). Also you need to consider the way you want your light projected. A direct beam can be good for focused work but can cause some harsh shadows. Using up lights or wall washes can give you the reflected light that makes the room seem more lit without harsh shadows.

Edit: something else to consider is CRI (color reproduction index). Try to find 90+ bulbs as those will ensure the colors it lights up look true to their originals. Makes a big difference especially if you're painting.

I watched a video a while ago where someone attempted exactly that. It's probably more elaborate than you're looking for, but the results are pretty great and maybe you can get some inspiration.

It might not seem like it, but you do need 5k to match the color of daylight. You'll also want bulbs that are 90 CRI like the other commenter mentioned. Lower CRIs can make the colors seem "washed out" which might be the difference you're seeing between your bulbs and true daylight. Multiple lamps would help as well, because otherwise the shadows will seem harsh.

I used a couple of full spectrum bulbs in my old west facing office and the lighting was perfect for my art. Have since then moved to another spot, need to set the bulbs up there too before winter. 😀

For getting the colour temperature just right: I have smart LED bulbs in my apartment, that can scan through a wide range of off-whites. If you get those you can dial it in without buying a bunch of different bulbs. They also have dimming so you can get the brightness how you want it. I would recommend getting 3 if you want a decent sized room to be bright everywhere. Not sure if that's a typo on "10 foot square room" since that would be less than 1 m^2 which is closet sized. Also I wouldn't worry about what colour you paint the walls as long as it's some sort of white.

I like lights that point up places in corners.

Artists like Ott Lights, my mom has one. They’re apparently very accurate

Paint the lower half of your walls in light blue, the ceiling in white, and the upper half of the walls make a very wide gradient in between.

Wait to finish your painting until daytime.