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This isn't too tough because the possibilities are few.

The multiples of 7 between 20 and 80 are:

21, 28, 35, 42, 49, 56, 63, 70, and 77.

Of these, when you add 1 ("next year") only one of them becomes a multiple of 5:

49 + 1 = 50

So my age this year is 49. 6 years from now I'll be 55.

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