Capster, the change in pressure is not that high. Rather less than what your car tyres have to hold.
Your car's tyre is at something like 50 psi total pressure - more after a long drive when the tyre has been heated by friction - the atmosphere around it is at ~15 psi (slightly less & variable so rounded for convenience) so the tyre's difference is ~35 psi. That 35 psi (or 32 or whatever you usually inflate your tyre to) is what we usually think of when we think about how much pressure the tyre holds. We tend to forget this measurement is relative to the atmosphere, not absolute.
Meanwhile, both relatively & absolutely, the shuttle's interior is held at 14.7 psi, the exterior is at 0 psi (near enough) so the difference is......14.7 psi!