By my calculations 5 miles a sec in 300 feet means an acceleration of 36000 G's. Sounds like you need a much longer tube if your not going to crush your payload into a pandcake!
During the component testing phase in the 1980s they tested everything that would go into the projectile up to 100,000 g's; only a delicate clock was fractured/damaged. As you may know, Gerard O'Neil at MIT did extensive work on the mass driver, getting short acceleration bursts at about 1,000,000 g's and finding out that ATTRACTION works much better at keeping the sabot/projectile centered than REPULSION. That then led to the idea of the quenched superconducting rings-concept : you turn each ring off, just ahead of the sabot-ring, with a lasar pulse. The only possible technical problem might be an AC current if the lasar pulse isn't precisely timed. Other than that though, there are no TECHNICAL problems, only NASA problems. There is of course a vacuum within and thus some 15 film-divided chambers at the top(1 psi differences)so that they roll to the next frame, like advancing camera film, when the sabot/projectile punches thru. The projectile nose has lithium pores, or cast-in Li beads, for ablation heating during the 2-3 seconds until the tropopause. We had it all worked out TECHNICALLY, VESTED INTERESTS at NASA shot EMSL, the freight train to LEO at $4/$....down....