Fill in the blanks using the numbers one through nine. (Based on Prof Layton's puzzle)

Note: Each number can only be used once and the equation must be "complete".

☐☐☐☐☐ – ☐☐☐☐ = 45556

:) Any help is greatly appreciated! I keep getting answers like:
54867 - 9321 = 45546
53968 - 7412 = 46556
54768 - 9312 = 45456

54872 - 9316 = 45556

I am sorry that I can't provide much of an explanation of how I reached that conclusion, but it works.

I'll try to provide an explanation if I can.

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This one was seriously annoying :)

I've got 52397-6841, tried a lot of switching to improve the result until I got it, so can't tell you a certain logic on how to work it out, hope I've helped.