Thanks to both of you.
NMinimize[{Abs[1/(x + 13328)^(5/7) + 1/x^(5/7) - 2/101325^(5/7)], x > 0}, x] gave x=95035.5. Thanks! Now I have a new way of inputing troublesome equations into wolfram alpha! Iteration on a calculator gave 95035.45649. Is it possible, with this sort of equation, and this method of input, to get 10 or more sign. figures from wolfram alpha?