555 How can I make a 15 minute egg timer circuit

To do this, I want to push a button to initiate the timer, which will then light 3 x leds. After each 5 minute segment is up, one of the LEDs should go out. Finally, when 15 mins is up, I want to ring a bell (just once) using a solenoid. Trouble is - I don`t know where to start! My background in more in computer programming - so I understand the logic required to do it,
555 How can I make a 15 minute egg timer circuit - schematic

just not how! (I`ve put circuits together in the past, but always using someone elses schematic - I`m not sure where to start in terms of designing my own. ) I`m not looking for someone to design it for me (though it might help!) but for an idea of where to start figuring out how to do this. Have had a look at some 555 based egg timer circuits, but don`t know how you set the time periods on them. Have knocked up a vague schematic - does it look like I`m heading in the right direction If this does what I think it does it should begin with three LEDs switched on, then with each clock pulse knock an LED off until they`re all off - then it should reset.

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