The big problem isn't going to be the freeze; sure that'll kill a lot of surface life (all of it if we're talking true snowball earth effect), but the equatorial regions wouldn't have that for the full 5 years. The real problem is going to come from the rapid temperature changes. 5 years to go from iced over to no ice at all is... incredible. You'd erode so much surface into the water that the term "topsoil" will be meaningless. Worse still, the rapid dump of meltwater will disrupt oceanic currents and destroy that thermal regulating system. You'll have hurricanes so powerful that "Class 5" won't be enough to describe it.
Humanity is basically a write-off at this point. Underwater dwelling is... hard. Very, very hard. Especially as you'll want to be below the thermocline to avoid the worst effects, and humans don't do well at that depth even with lots of equipment. Space it an option, but Oneil cylinders would be expensive to build, and hard to maintain; albeit more feasible than ocean-floor arcologies at our current engineering capabilities.
If we assume Kardashev 1 civilization, we could presume orbital solar arrays being used to gather solar energy and beam it to the earth to control the runaway climactic shifts. Beam more energy to heat the surface during the cooling cycle, and less during the warming cycle, combine that with high-atmosphere albeido-adjusters and you could geo-engineer a stable temperature gradient.
You could also create boreholes and use geothermal temperature regulation, geothermal power, artificial lighting for crops, and nuclear or thermonuclear generation to supplement the geothermal (you'll need it, humans use a lot of power). Overall though, unless it's a cycle that will stabilize in an unbelievably short timeframe (100 to 1000 years), you're still talking complete human extinction.
So.. Space habitats... huge, self-sustaining, repairable, space habitats. Or global scale geoengineering.
Would be neat to see the orbital pictures of Earth, devoid of anything like surface life and nearly completely obscured by multiple simultaneous Class 5 tropical cyclones though.