I wouldn't bother with a microcontroller, some other simple ways:
1. Use a 74LS123/4098B (dual retrig monostables), set one half at 1 minute and the other at 5mins. No programming...
Look at Fig 15:
http://www.rapidonline.com/pdf/83-0426.pdf2. Perhaps if I wanted more stability (using smaller low tempco capacitors) I might use an astable configured 555 timer, a divider (such as 4020B/4040B) and a 4017B (configured as a 1:6 divider).
3. If you have a handy secondary of a transformer around, then tap off (via a 1M resistor and a zener) the 50Hz, feed it into a chain of 4017B's set as simple dividers (10, 10, 10, 3) then feed the exact once per minute pulse into another 4017B (configured as a 1:6 divider).