An LED is a very nonlinear load. It may be 5v at the rated current, but only 5.25v at twice the rated current and 4.75v at half the rated current.
So, you might be able to assume that no matter what the current (within reason), the LED is around 5v. From there, you assume there's 7v across the resistor and you can choose a resistor size that creates the desired current.