In the 15 years or so that I've been trying to go to test matches, our names go into a ballot and if you're lucky you'll get tickets for one day, and one day only. Most years I've managed to get tickets with a group of mates, but there have been some years when that's not the case and we've not been lucky enough.
(this is my experience of the Oval and Lord's mostly, and for the bigger or better touring side of a summer if more than one has been here).
The idea of someone even getting the chance to see more than one day, let alone all five days, just doesn't happen most of the time. By the Test grounds limiting you to see one day's play they can maximise the number of people seeing a test match - they are not going to allow individuals to see more than one day's play when there is so much demand for the tickets.
That said, for the early-summer tests against the likes of Bangladesh they rarely sell out in advance, in which case they sell tickets on the gate on the day of play itself, so there is nothing stopping people from turning up on the day and watching as many day's play as their wallet can cope with.
I do agree however that if a ground is struggling to sell tickets, even with people turning up on the day, they should make them cheaper, or offer cheaper prices for those getting in after tea for example.