Find the smallest natural number starting in the decimal notation with a five, which decreases four times if you erase this five

Find the smallest natural number starting in the decimal notation with a five, which decreases four times if you erase this five from the beginning of its decimal notation and add it to the end.

Let us find the smallest natural number that begins in the decimal notation with a five and decreases by four times if we erase this five from the beginning of its decimal notation and add it to the end:

the first was 5, so when dividing by 4 we get 1, then the next digit is 1;

51/4 = 12;
512/4 = 128;
5128/4 = 1282;
51282/4 = 12820;
512820/4 = 128205 – found the required number.

Answer: the smallest natural number that starts with five and decreases by 4 when carrying 5 to the end: 512820.