I wonder if I should earn a bit more by working for a while, how much did you have when you started ?
$450 rent, $300 utilities (power, gas, water, sewage, data data data), $100 gym, $500 health + pension, $250 food + sundries if I live the cheapest I have ever achieved living. $750 on food and sundries if I live how I actually live (e.g. eating out, entertaining, going out with friends, what have you).
Hard times!
90% of UK businesses fold in the first year, I can see why.
Basically the message was, sit and do nothing and we'll give you a house and pay you unemployment (until your payed in years of NIC have run out at least). Start a business on credit and we'll let you starve.
It's only something I can recommend to a certain kind of person, but the experience of crawling out of that does give a person a certain kind of strength.
Your question is a fine question to ask but, unless you provide more context, there is no way that nearly anyone with experience will want to spend the time working through all the possible data points.
If you want to do your own project full-time, make an estimate as to how much it costs for you to live in your area per month. $1000? $2000? It's hard to say because it will depend on where you live. Set aside 12 months worth of cash (6 months for dev time and 6 months to give yourself some time to make money after launch) and maybe a little extra for emergencies, and get to work!
Of course this is assuming you think you can become ramen-profitable in 6 months. Many people haven't become ramen-profitable in years, or ever. It depends on what your living expenses are and how you are monetizing your project.
Teaching English in China can get you that 400 USD rather quickly. Also, if you can do basic web development, you're pretty marketable (this pays relatively better than English, but English jobs are possibly easier to find than software consulting).
Unlike a lot of people starting a business, I had almost no fear of starving on the streets. When it comes to ensuring that I both have food and own as much of my time as possible, I try to eradicate risk as thoroughly as possible. Having a minimal financial footprint and redundant contingency plans allows me to do that.
Thankfully, these days, I don't need the side-jobs, I mostly just focus on growing my business's profit. When I want something unusual (new monitor, new advertising campaign), I just sleep a little less and pull in the extra money with some software consulting.
You can call it the lazy loading approach to finance.
That's a calculation only you can do with your current living costs in addition to estimated cost of equipment, services, software, office space, and probably lots of other things you would never imagine (legal costs, accounting costs, cost of incorporating for example?)
If you're asking the question then I guess you haven't done these calculations yet - but putting them all down on paper (or spreadsheet more appropriately) as well as a realistic development timeline will tell you what you need to know.
Good luck! If you never try you'll never know.
However, what we did have was a contract from a client giving my co-founder and I a years guaranteed work. In that year we found enough additional work to raise the headcount to four people and be fairly profitable - which we used to support the work required to eventually get VC investment and switch to product development. We got our first round about 2 years after we actually started trading.
As a side not you will probably lose the money, but the learning experience will be invaluable :) From what I understand sounds like your burning rate should be pretty low. $5k could be enough. The risk seems minimal. You are just out of school, not leaving any kind of high paying job (anyways, you can always find one if you fail). The worst case scenario is losing that 5k.
You can do it!
Also, have a good cofounder. You might have heard this many times but this is true. A good cofounder will take away some burden from your shoulders and you will keep you motivated.
If your idea works out, its good. If it doesn't, not a big deal. You will have learned alot along the period of time which will help you get better job than you would have got when you graduated.
Two lessons I learned: we should have invested more money in the company and had more money in reserve. If I was doing it again, I would not be comfortable without at least 1 year of living expenses.