Laura, welcome aboard!
It's not often that somebody starts by specifying their target as some number of microns per pixel, so immediately I'm wondering exactly what's driving that specification.
I assume that it relates somehow to the size of detail that you want to resolve, but then I wonder if you have already factored in the impact of Bayer filtering and assorted degradations due to spatial sampling.
As a general rule, to get reliable rendering, you'd normally like to have at least four pixels per cycle, each "cycle" being a black/white line pair so that BWBW would span 8 pixels. Some illustration and discussion of why this is so can be found at
http://www.photomacrography.net/forum/v ... php?t=2439.
Anything further you can say about what you're really trying to accomplish would be helpful.
For the image that you've posted, you wrote that "SOOC there are 2.5um per pixel". I assume that SOOC means "straight out of camera". But the image as posted is different from that. I measure it as 290 pixels for 1000 microns, which would be more like 3.45 microns per pixel. If you can explain that discrepancy, it would also help a lot.
Now, taking your "less than 2 um per pixel" as an appropriate spec, and noting that the D5300 has pixels that are 3.92 microns wide (23.5 microns sensor width, divided by 6000 pixels), it seems that you're needing at least 2X magnification, which would give a total field width of 11.75 mm.
Getting pixel-sharp images all across an APS-C sensor at exactly 2X is actually a pretty challenging problem, so it will be helpful to know if there's some "give" in your specifications.
For example, if in fact you only need to cover a field that is 4 or 5 mm wide, then the obvious approach is to go for an optical magnification someplace in the range of 4X to 5X, for which low power microscope objectives are a good match. If you need a sharper image, and you can live with per-shot DOF of only around 8 microns, then you can even use certain 10X microscope objectives and push them down to 5X by using a shorter than normal "tube lens". See
Lenses for use at 4-5X on an APS-sized sensor for a range of possibilities. BTW, the basic reference on using an objective with a DSLR is our
FAQ: How can I hook a microscope objective to my camera?
If your subjects are 3-dimensional, then most likely you'll be needing to use "focus stacking" in order to get everything sharp. That in turn implies that you'll need to have some sort of focus-stepping mechanism capable of movements in the range of 5-50 microns. There are several good mechanisms to do that, both DIY and commercially packaged, but of course there are impacts on the budget. What is most appropriate will depend on time/cost tradeoffs, basically how many subjects you want to image, and how quickly.
I apologize for raising so many different issues, but there really are a lot of different facets to the problem. Again, anything further you can tell us about your application will be helpful.
--Rik