Andorra is what you get when two medieval powers can't agree who owns a patch of mountains and decide to share it. A treaty of 1278 split the valleys between the Bishop of Urgell and the Count of Foix, whose title later passed to the French head of state, so Andorra still has two heads of state, and neither lives there. It has no airport, no railway and no armed forces, 468 square kilometers of which only 8% is built up, and one language by law, Catalan. It adopted its constitution only in 1993. In winter it also has the largest ski area in the Pyrenees.
That mix is the character of the place. The pass covers three ski areas, and the base villages are practical rather than pretty: hotels, ski shops and duty-free stores, with Romanesque churches tucked between them. Five days is the right length because Grandvalira is a ski area you learn sector by sector. Three ski days there, a day at Pal Arinsal and one day off the skis in the valley is a rhythm most legs can take.
The plan runs like this: day one is Soldeu and El Tarter, day two Grau Roig and Pas de la Casa on the French border, day three Encamp, Peretol and Canillo, day four a break from skiing in Andorra la Vella and Escaldes-Engordany, and day five Pal Arinsal on the same pass. Start skiing on a Sunday, after arriving on the Saturday: the museums in town are closed on Sundays and Mondays in winter, and a Sunday start puts the off-ski day on a Wednesday. There is more about the country in the Andorra country guide.