Estimates, deadlines and milestone

I am currently learning agile with a focus on project planning. I am having some issues aligning the teachings to the real world.

With agile I have learned, that we need to get customer feedback in every iteration, and we should include this customer feedback into our backlog so it is address, and we give the customer what they want. Secondly there is the cone of uncertainty, which says that my estimates can be 4 times higher or less. This all seems fine but it makes it very hard for me to figure out how I should report on the project.

Let’s take an example from a project that I am currently working on the currently projects completion data is 5 months from now. With the cone of uncertainty the means it will take between 1.25 and 20 months to finish. With a hard deadline of December 1, 2019, should I tell my management no way! I can first have this done Jan 2021?