Invention Help. Need 8 hour delay off with 5 minutes on and then repeat

Hi, I'm working on a project that I need help with. First off, I am a newb at this sort of stuff, so sorry in advance for my ignorance. I'm a biologist working on a simple device. I need to turn an airpump on for 5 minutes and then off for 8 hours. I think I can construct something of value with this, if I could pull it off super cheaply. So I've been doing some searching online and getting familiar with electronics, and I see that a microcontroller of sorts is what I need. An arduino might be overkill for my application but I do not know. So.....

What it does and what's needed.

1. A battery powered device that when turned on will turn on a pump every 8 hours for a duration of 5 minutes. Then it repeats. Simple on off toggle switch to activate.
2. Needs to hook up to an air pump. I have no idea what to buy here. Do I buy any battery powered air pump? Is there a specific air pump that is designed for Arduino or other hardware specific to what I need?
   3)So there must low power requirements but have enough capacity to power an air pump when on the "on" mode for the 5 minutes, and be able to repeat many many times

I don't even know how to state some of the questions I have. Like how exactly can I make it battery powered, what parts do I need, and what is the feasibility with regards to cost. I am completely clueless to electrical engineering or computer programing. Also I'd like the whole project to cost under $20 for each one.

Any help, comments would be appreciated.

How accurate does the timing need to be? 8 hours give or take 10 minutes?

How much air (volumn & pressure) do you need?

Under $20? that probably going to be a problem.

You need to define your specifications so you can then do some web searches and see what might be available.

It doesn't need to be accurate, give or take 10 minutes is fine. it can even be a 6 hour delay, and turn on 4 times a day instead of 3. What specifications do you mean? Like what kind of air pump? The cheapest aquarium pumps would work fine, so I'm not concerned with any pressure problems. Even if it pushes air out at a couple psi, that would work.

Is it really gonna cost that much? I need to build prototype anyway, but yeah, I'd like to eventually get the electrical components under $20 bucks.

I've researched things like the 555 timer, which isn't suitable for long delays.

Is there a specific air pump that is designed for Arduino

I guess your local aquariums supply shop does (not yet) have these on stock

It sounds to me as if choosing a suitable pump and providing a suitable power source for it are your main problems. The control side with Arduino would be straight forward but finding a cheap battery powered pump with a decent life might be tricky.