I'd get MUCH faster than that simply by tethering my laptop to my iPhone and using the 3G.
I just ran Speed Test and my 3G connection returns 20.19Mbps down and 13.85Mbps up.
I almost never use hotel wi fi unless it is free or very cheap. However uploading the amount of data you are talking about would be expensive - my mobile plan (like most NZ plans) is data capped. My included limit is 2.5Gb/month. Over that and you're paying 20cents a Mb.
Yeah, the issue will quickly turn into one of cell phone data limits/charges if the OP is really trying to transfer 2-5GB every few days. If I had to xfer that much data and had such a poor hotel connection, I'd first see if the hotel lobby provided better connectivity (sometimes, you just have poor wireless reception in some rooms, but the lobby is more optimized for wireless reception) and then, if not, I'd seek out a nearby Starbucks for better connectivity. Starbucks are not all universally fast either, but are usually better than many hotels in my experience.