That circuit looks good -- connecting all the 5V connections together to a single 5V pin.
In the case of trying to use a single resistor, I'd suggest 15 times 220 Ohm, or 3.3k Ohm, but in that case, you would not be able to read changes in each sensor separately. That is, you would not know which sensor had changed resistance, only that the overall resistance had changed (you'd only have one analog input, after all).