Woah! 7 is so cool!

Number Theory Level pending

Find the least number whose last digit is 7 and which becomes 5 times larger when this last digit is carried to the beginning of the number.

Details and assumptions:

You're not adding any 0's or any other digit when you shift the last digit to the beginning. So for example, say the number was 321157, then after the shift, the number will be 732115.

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