I'm not going to say rates won't shoot up to 5% in two years but it is extremely unlikely.
I know you probably feel this way too and are just playing it safe with your comment, but I'm happy to come right out and say there's no chance of that at all. It would crater the economy that's been struggling for years. If it turns around, it will be moderate at best and they will let it run for a little while before putting the brakes on, and brakes will come in the form of .25 here and .25 there. That's 10x .25% increases (one every time they have a rate review) before we get to where variable would be 5%.
The argument seems to go like this right now: even though historically it has always been cheaper to go variable, this time is different. But it was historically better to go varible when rates were 18% or 10% or 5%. So why wasn't the same argument proven true when it went from 18% to 5%? The spread was lower than ever at that time too. Rates were so cheap! Now it will prove to be historically better to varible at 2.2%. The game is the same; the banks charge you a premium for peace of mind. They are not giving anything away, and you are likely to be wrong if you try to 'outsmart' them by betting against their rate forecasting which is exactly what you are doing when you fix your rate.
If the banks thought there was a snowballs chance in hell of rates going up by more then 1% in the next few years, they would not be offering fixed rates at around .5% over variable.