As others have already noted, using decimal notation as a base here is problematic in many ways. I'd suggest seximal (base 6) instead. I'd also shift the digits by one, so have 1-6 instead of 0-5, because having empty ring for 0 is not good. The rings also need to be rotated by 30° relative to each other so that "2"s do not overlap like they do now.

60 in base 6 is 140, so in theory you'd need three rings for both minutes and seconds. But because that highest digit can only be 0 or 1 I think there would be other ways to represent it, so you'd manage with two rings. One option is to reverse the colors (/fill the ring).