I think it’s a promising way to tackle this problem overall, I started the same way 
But there is a logical error in your reasoning. 14.4 sensors means that it is certainly not possible to cover the area with less than 15 sensors.
Meanwhile, 15 sensors could theoretically cover 15*5 = 75 squares, which is more than we have.
So we inevitably come to the question of exactly how to put the sensors. We have already proven earlier that it is possible to do so with 18. So the answer is somewhere between 15 and 18.