Irkutsk was founded in 1661 as a fort, grew rich on the China trade and Siberian gold, and burned badly in 1716 and again in 1879, when the damage took more than ten years to repair. After the Decembrist revolt of 1825 it also became a place of exile for officers and nobles, and by the late 1800s about a third of the town's people were exiles. They built schools, theaters and carved wooden houses, and around 1900 the city was nicknamed the Paris of Siberia. The Trans-Siberian railway passes through it, and 66 km away lies Lake Baikal, the deepest lake on earth at 1,642 meters, holding more fresh water than all the North American Great Lakes together, and on the UNESCO list since 1996.
The city is a day, and the lake is the reason you came. Baikal is big enough that where you stand decides what you see: the Listvyanka shore is a short ride from town, the old Circum-Baikal railway hugs the southern cliffs, and Olkhon, the largest island in the lake, is a long day's drive away. What you can do depends on the season more than anywhere else in this series. From mid-May to autumn the ferry to Olkhon runs and the water is open. From about January the lake freezes, and the ice road to Olkhon only opens when the ice is thick enough, usually in the second half of February. November is in between, which is the worst month for logistics and a quiet one for crowds. Five days gives the city one day, Listvyanka one, the railway one, and the last two Olkhon, with the drive back on the morning of day six.
Day one is Irkutsk on foot, day two Taltsy and Listvyanka, day three Slyudyanka and the Circum-Baikal railway, day four the crossing to Olkhon and Khuzhir, and day five Cape Khoboy, with a second night in Khuzhir and the road back on day six. Start on a Wednesday: the Volkonsky house museum is closed on Mondays and the Trubetskoy house on Tuesdays. Read the visa and advice tips before you buy anything, because for Russia the paperwork and the cards come first. For the country as a whole see Russia.