Yes, that's usually what you get when you are requesting something out of proportion. Don't you notice that? Web hosting of 5GB diskspace aren't selling for peanuts so I doubt you can find a webhost giving you that for no ads or 30 forum posts. If you find one, it's highly likely that the webhost is going to be unreliable, maybe even going down within a couple of months.
Also, if your website is not an existing website, it hardly justify your need for 5GB which is freaking a lot to ask for. So, my advice is to reconsider your requirements and go for something that you really need, not an imagined future requirements of a website that got really popular.