Hey there!
It's difficult to predict this in reality. In fact, it's almost impossible.
If we look at the company's earning history over the last 4 years, it's more than tripled its bottom line. So, if it can continue to do this, there is no reason to believe the dividend growth couldn't continue.
However, it would be naïve to think they can grow earnings at this pace as well.
The only thing we can look at now, is the company's outstanding record of growth as of late and the fact it still has a good chunk of room to grow the dividend with it paying out less than 1/3 of earnings towards it.
Lets assume your 5-7 year thesis is correct.
The question I'd have to ask you is would you really be disappointed if the company managed to increase its dividend at a 40% pace for that time period and slowed to say.... 15-20% growth?