Seven's Cycle Sum Sequence
Python 2, 69 bytes

lambda n:[''.join('02'[x&gt;'0']for x in`n`)+'0',n][set(`n`)&lt;=set('05')]

The function is simple to describe:

If n consists of only 0's and 5's, output it unchanged.
Otherwise, replace each digit of n with 2, except 0 stays 0, and tack on a 0 to the end.

The golfing can be improved, I'm mostly posting to share the method. A language with native regex should allow a short solution.
An alternative statement of the function is

In n, replace each digit with a 5, except 0 stays as 0
If this changed n (it had a digit other than 0 or 5), multiply the result by 4