Greetings Jacob, I am sure you are aware that Instagram is a VERY popular and big Application, so even along website cannot be done in US $5,000, as thesis VERY low budget but you want both iOS & Android App too. So, here is how you can move forward.
You can work in few phases, so in 1st phase, please provide me list of basic features, and I can give you our firm estimate. After this 1st phase, you can continue adding as many features as you want down the road unless you have BIG budget to start whole project at once.
You may ignore the bid amount for now, as we still need to discuss & ask questions.
Look forward to hearing from you.
Regards,
Yasir
LEADconcept
PS: Please let me know, if you want to see some of our recent portfolio.