Riddle me this

So, I bought a new book recently, The medieval puzzle collection. 

Frustratingly, it has no actual references to anything historical so goodness knows how actually medieval it is.

It sounded fun however so here's your first puzzle. Check back tomorrow for the solution.

Alcuin, the abbot of Marmoutier Abbey, was greatly fond of intellectual challenges, and had become known far and wide as a fierce scholar and teacher. One afternoon, he called his students into his office, and indicated to them five numbered stacks, which, he informed them, held grain.

"Pay attention," he said. "Each of these sacks contains a different amount of grain. Taken together, 1 and 2 weigh 12lbs. Similarly, 2 and 3 together weigh 13.5lbs. Numbers 3 and 4 weigh 11.5lbs. The last two sacks, 4 and 5, collectively weigh just 8lbs. Finally; it will be useful to know that sacks 1, 3 and 5 together weigh 16 lbs.

What is the weight of each sack?"

Notes
Dedopulos, T., The Medieval Puzzle Collection (London, Cartlon Books Limited: 2014) p. 17

Image - Two merchants negotiate terms to barter wool for cloth, Biblioteca Riccardiana (Florence, Italy), Ricc. 2669, page 66 r.