In reply to Kemics:
I went to the Picos a few years ago with the same idea: walking between Lagos de Covadonga and Fuente De in 5-ish days. We ended up re-adjusting our plans after a couple of days. As Niek said, there are very few water sources, and the ones that are there tend to be next to the huts. You can camp near the huts, but that was not really the wild camping we were hoping to do. Also, the Cares Gorge running through the middle of the Picos, means a big descend & re-ascend if you want to traverse the area. We knew this, but hadn't quite appreciated how steep the descent was: we had full packs and I struggled to walk the next day due to sore muscles. As a result we decided to leave our camping stuff at a hotel in Poncebos, and then walked through the Eastern Picos for a few days, staying in huts.
It's an amazing area, and definitely worth spending a number of days walking across. If I'd do it again, I would plan it as a hut to hut trek. Lightweight approach made the second half of our trek far more enjoyable. I think the huts are about 12.5-15 euros (cheaper with a membership card), with dinner also costing that much (but there is lots of it!). Lunch was rubbish, bring your own & save the money.
We used these maps (top 2:
http://www.thepicosdeeuropa.com/national-park/maps ) and found them very helpful. Paths are mostly marked, but can be difficult to find sometimes.