Even in 2005, mobile internet was so shit, it might as well not have existed. 2007-2008 was when 3G was starting to get rolled out I believe, but even that was pretty damn slow and expensive. 3.5G in ~2010+ is when things were usable enough that you could perform a Google search without giving up before the your first result loads.
WAP was a bit of an attempt, but in truth you couldn’t do much of anything with it.