It is bad to do an (almost) empty loop to spend some time (CPU bound), and it is bad to flood the console too (here with 5000 lines), as it can bring down the PDE.
One solution is to use delay(), at least it won't lock the PC. But it will freeze the sketch, which isn't friendly.
Another solution is to do nothing in draw(): since it is called several times per second, it is the body of a loop itself.

Using the second solution:

1. int x;
2. void setup()
3. {
4.   x = millis();
5. }
6.  
7. void draw()
8. {
   
9.   if (millis() - x > 5000) { // Notice I inverted the test!
10.       println(x); //space for my calibration routine to collect sensor data
11.       x = millis(); // Reset the timer
12.   }
13. }

You should use a better name for the variable (x is often used for coordinates), like startingTime or similar.

a) You need to put a sleep inside the loop or else it will overload the computer with nonstop IO attempts. By the time the while loop is actually exited, there are so many calls to println that your computer has locked up.

The IF statement route is good but my problem is that I need it to sit in one loop reading sensor data and analyzing it for about 5 secs before moving on to the rest of the program.  I have been using flags to get around this...

" I need it to sit in one loop reading sensor data"
Well, as I wrote, draw() is the loop you need...

Indeed, using flags is a way to do things sequentially. That, or a state variable, indicating by a number at which step you are.
Using functions can help in modularizing the code and making it more manageable / readable.

delay() is back in latest versions of Processing. Not sure it was a good move, since I felt it should have been renamed to Serial.delay(): that's probably the only place where it is really needed...

Actually, delay() is just a convenient wrapper around the Thread.sleep() method.