When learning option strategies there is a tendency to view the strategy as the engine which drives the profits or losses rather than the correctness of one's ability to predict price movements. This is likely due to the fact that it takes time to grasp the nuances of the strategies and we focus on what we have spent our time learning.
In this case we are looking at the following idea: Buy the 100-105 call spread. If the price moves up to 105 then buy the 105-110 call spread, leaving us long the 100-110 call spread. You seem to have a grasp of what the new position offers. That is, the potential to reap the 10 point spread between 100 and 110 instead of the 5 point spread between 100 and 105, less the cost of putting the trade on.
But doesn't the question really hinge more on your expectations for the price movement of the stock? To enhance your knowledge you may want to run some numbers on different possible outcomes over time, given those expectations. Then I would recommend learning more about the impact of implied volatility changes with particular emphasis on vol skews and how they impact the position and what they reveal about market expectations.
Bear in mind that the more options you trade the more transaction costs you must overcome in order to be profitable. Commissions and spreads add up.
Finally, another simpler and different approach, depending again on your expectations, is to buy the 105 call. Should the price move to 105 then sell the 105-110 call spread leaving you long the 110 call. At that point you will have little to lose and retain the potential for further gains if the upward price movement continues. Just a thought.