Try a free web hosting provider like 500megs.com but you will DEFINITELY not get any free hosting with 5000 MBs of space.

If you need that much, go for a paid one.

I read about a host which offered 10000 MBs of free webspace and 100 GBs of data transfer per month unless your site doesnt volates their TOS and AUP.

I dont remember the URL now but if I get it, I will surely post here.