Perhaps not a total fix, but some ideas in hopefully a helpful direction.

I doubt the noise is camera noise at 100 or 200 ISO, if you are completely filling the frame of the D5000. My D5500 is newer, but I'm almost sure it couldn't be that much noisier than mine.
It is, btw, just about fixable in Photoshop, pic at the end of a quick 'fix' attempt.

To fix your focussing issue, shift the camera to Live View, then use the + [magnifier] button bottom right to zoom in as far as you can. Adjust manual focus whilst you can see one of the hardest-edged details in your slide.
[I've subsequently seen the new question & don't know why the reversing ring can't focus… unless it has no electrical connections]

You have some vignetting [a darker ring round the edges] - possibly because your diffuser isn't absolutely 'perfect' or your light source is too close behind it, or indeed that the lens itself [not designed to work that way round] is vignetting. You may not be able to fix this entirely, but you could perhaps swap out the tissue I previously suggested for some proper diffuser gel. You can get this for just a few $£€ on eBay. It is, comparatively, optically perfect. It may still not be quite enough to get rid of all the vignetting. This can anyway be fixed in Photoshop to an extent.

You also have a purple-ish colour shift. this might be the film or it might be your white balance, or even the LED. Probably film. It may well change between film batches too.

With some Photoshop 'magic' you could actually work out how to automate all of this - but that's definitely for another question [& someone better at Ps batch scripting than me].

Anyway - a quick attempt to smooth the noise, pull back some of the purple, punch up the remainder, knock back some of the over-bright centre & balance out the vignette. [It's not perfect, it's a 5 minute quick fix.]

eBay UK link to an example gel diffuser (not a recommendation, per se)