To understand the flow, let us put a print statement in the code:

int i = 1, j = 10;
int k =1;
   do {
      System.out.println("Iteration "+k+": i=" + i + " j=" + j);
      k++;
      if (i++ > --j) continue;
   } while (i < 5);
   System.out.println("i=" + i + " j=" + j);

It generates the following output:
Iteration 1: i=1 j=10
Iteration 2: i=2 j=9
Iteration 3: i=3 j=8
Iteration 4: i=4 j=7
i=5 j=6

In the iteration 1, the if comparison goes like this: if (1++ > --10 ) continue; => if( 1 > 9 ) . The values of i and j after the if statement are 2 and 9

In the iteration 2, the if comparison goes like this: if (2++ > --9 ) continue; => if( 2 > 8 ) . The values of i and j after the if statement are 3 and 8

In the iteration 3, the if comparison goes like this:if (3++ > --8 ) continue; => if( 3 > 7 ) . The values of i and j after the if statement are 4 and 7

In the iteration 4, the if comparison goes like this: if (4++ > --7 ) continue; => if( 4 > 6 ) . The values of i and j after the if statement are 5 and 6

Now, i is not < 5 so the while(i<5) check fails and the loop terminates. So the final values are 5 and 6.