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Not in a way that would be generally understood. However, it is possible.

An 8-digit number in base 10 can be represented by a 5-digit number in base 32. For example, extending the scheme for labeling digits for base 32,

VVVVV32 = 3355443110

Similarly, the 8-digit number 33333333 in base 4 is the 5-digit number 65535 in base 10

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Q: Can you represent an eight digit number with a five digit number?

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the number is -49999,5 42857 428571 = 3 * 142857

Definitely earlier than the year 2000. In April 2000, Portsmouth moved from six-digit local numbers to eight-digit numbers, as well as changing to the new, short area code of 023. (For example, Portsmouth City Council's number changed from 822251 to 92822251.) Instructions at the time referred only to how to convert six-digit local numbers to eight-digit numbers, so it is reasonable to assume that no five-digit numbers remained at that time.