Without knowing the specifics (grain bill, yeast strain, mash temp, pitch rate and dissolved oxygen amounts), I'd say you're finished, especially since it's been 5 weeks. Have you measured a drop in FG over a few days time? If not, I'd say you're definitely finished with that initial pitch.
1.035 from 1.120 isn't bad, it's nearly 71% attenuation, which is pretty good for such a large beer. Consider that the beer is around 11% alcohol, which is a toxic environment for a lot of yeast strains.
Getting large beers to ferment low is a challenge. Common tips are to pitch the proper amount of yeast. This beer needed around 600 billion healthy yeast cells for a 5 gallon batch. Also, its recommended to inject pure O2 prior to inoculating and around 12 hours after inoculation to ensure there's enough available oxygen for the yeast to synthesize sterols and fatty acids in order to build strong cell membranes. It's also common to turn the heat up after primary fermentation has slowed down to really crank out those last few points to increase the yeast activity.