Many Tears is a rescue centre near Llanelli which mainly rehomes dogs saved from puppy farmers. It's a sobering read: they prefer to rehome ex-breeding dogs where there's an existing dog, because the ex-breeding dogs have no idea how to interact with humans or live in a home, as they've had little or no contact with kindness or pet routines, and need another dog to teach them. 
Not all adult dogs are given up for rehoming because of temperament issues. Many - especially those in Basset Welfare - are given up because of divorces, house moves, job changes, the arrival of kids, or illness, and if the owner is responsible enough to hand the dog in to a breed rescue, rather than just put them in the small ads, hopefully they've been cared for and well-trained. Bassets are often surrendered because the owners didn't realise they needed so much exercise, or that they'd grow so big, or be so loud or so 'houndy' - none of which are the dog's fault. And some 'temperament issues' - bounciness, attention-seeking, separation anxiety, etc - can be sorted out with regular walks or consistent training. So don't be put off!
But, to be honest, five hours is too long to leave a Basset on its own - it's too long for any dog, really, but Bassets need company. Would that time include your travelling to and from the school? I work from home, so am around most of the day with my dogs; we do a long walk at lunchtime, and if I have to go out, they're happy to be left together for a maximum of 3.5-4 hours, with the television on and a Kong to chew. If I have to be out longer, I leave them with the dog sitter. Could you get a dog walker to come in and break up the five hours? Or a neighbour? Or a dog owning friend?