I'm not sure a tilt-shift on a crop-frame would work out anyway. Nikon makes a 24mm, 45mm, and 85mm tilt-shift (they call it "perspective control" or "PC"). Schneider makes a 28mm (two actually) and 90mm. All of those will be in the "thousands" of dollars price range.
Rokinon has a budget tilt-shift... 24mm f/3.5 in Nikon mount for the bargain basement price of $759. Roger at LensRentals says it's decent when stopped down to f/8... but if you plan to shoot f/3.5 you probably want the Nikon lens (so apparently you don't get the quality of a $1700 Nikon lens for $759 from Rokinon -- no big surprise there.)
On an APS-C body such as your D5300, a 24mm isn't particularly wide (a "normal" angle of view is close to 28mm -- so this is just a few millimeters wider.) If these are large/tall buildings then you'll need to be able to back up quite a bit -OR- you'll need a much wider angle of view than a 24mm can provide. (Canon makes a 17mm tilt-shift, but I think they're the only company that has a really wide TS lens.) On a full-frame body, 24mm turns out to be a fairly nice angle of view for this sort of thing... but you don't have a full-frame body.
The biggest feature of "tilt shift" lens in architecture is ability to use the "shift" (in that mode the lens doesn't tilt... it just slides sideways to go off-axis) to control the perspective that buildings have where things tend to look like they are "leaning" backward on you.
It turns out, you can use Photoshop to perform such a correction... either through the Lens Distortion menu or through a "Transform" operation (two ways to do it that I know of.) When this operation is performed, the image is stretched and pinched into a trapezoid ("keystone") shape and that fixes the perspective problem -- and then cropped back to a rectangle so that it looks like a normal photo.
If you know you're going to have to perform such an operation, you need to leave a lot of extra space at the sides of the building -- knowing this will be cropped out of the image when you are finished manipulating it in Photoshop.
Knowing this, I'm thinking you should go for a wide-zoom and use Photoshop to correct the perspective later.
I'm not nuts about stitching together panoramas because the lens angle changes between each shot (tilt-shift lenses can actually make panoramas that don't look like panoramas because the lens shifts sideways but maintains the same direction. )