Creating An Auto-sorted To Do List

Hey everyone!

I want to create a task/project list. This will be pretty straightforward, but I'm curious on a certain aspect. I have 5 main categories of work I do, so I want to keep them as separate lists in tabs (at the bottom of the worksheet). However I want a Master List that automatically pulls from the tabs so I can see all the work at a glance, but sorted by A, B, C, D priority.

I figure I can set the priority on each item as I enter them on their respective tab, but I want the Master List to automagically show everything in order. How do I go about this?

NOTES:
Each tab requires the same info per item – Priority, Name, Due date, status, requested by, and project notes.
I'd like for the Master List to show all the same details, just sorted so I can enter items in each tab and have the Master List update the order on its own.

Thanks for reaching back out to me so quickly. I didn't think to have the Master List push to the category lists. It sounds useful, I'm just wondering how inputting new items would be sorted in the Master List.

For example, in 3 weeks, I'll get say, 15 new projects. Adding them to the bottom of the Master List is not what I envisioned, more the Master List stays ordered by A, B, C, D priorities regardless of when the items were added or due.
I hope that makes sense.

If that can be achieved with the spreadsheet you graciously attached, then count me in!