I don't have an Android device, so it is quite fast on my computer...
I tried to address some inefficiencies, while playing a bit with your code, changing a bit the rendering. Of course, restore your own. If you do, move color() call outside of the loop, you can save some milliseconds...
I made draw() empty, as there is no point in drawing the rectangles over and over. Not really an inefficiency, but showing better the structure of the code...
I tried to use load/updatePixels instead of set(), known to be less efficient.
And I used Java's sort of arrays, instead of your bubble sort... One of the worst existing.

1. float[] px = new float[0];
2. float[] py = new float[0];
3. float[] distance = new float[0];
4. color backgroundColor = color(155);
5.  
6. void setup()
7. {
8.   size(800, 480);
9.   rectMode(CENTER);
10. }
11.  
12. void draw()
13. {
14. }
15.  
16. void mousePressed()
17. {
18.   // add new point
19.   px = append(px, mouseX);
20.   py = append(py, mouseY);
21.   distance = append(distance, 0);
22.   if (distance.length<2) return;
23.  
24.   loadPixels();
25.   for (int y = 0; y < height; y++)
26.   {
27.     for (int x = 0; x < width; x++)
28.     {
29.       // calculate the distance between the pixel and each point
30.       for (int i = 0; i < px.length; i++)
31.       {
32.         distance[i] = dist(x, y, px[i], py[i]);
33.       }
34.       Arrays.sort(distance);
35. //      sortDistance();
36.       float diff = abs(distance[0] - distance[1]);
37.       color c = backgroundColor;
38.       if (diff <= 5)
39.       {
40.         c = color(255 - 20 * diff);
41.       }
42.       pixels[x + y * width] = c;
43.     }
44.   }
45.   updatePixels();
46.  
47.   // rendering points as rectangles
48.   fill(#AABB55);
49.   noStroke();
50.   for (int i = 0; i < px.length; i++)
51.   {
52.     rect(px[i], py[i], 10, 10);
53.   }
54. }
55.  
56. void sortDistance()
57. {
58.   for (int i = 0; i <px.length-1; i++)
59.   {
60.     for (int j = i; j < px.length; j++)
61.     {
62.       if (distance[i] > distance[j])
63.       {
64.         float d = distance[i];
65.         distance[i] = distance[j];
66.         distance[j] = d;
67.       }
68.     }
69.   }
70. }

Also dist() is costly, computing a square root. Since you only compare the distances, perhaps you can avoid the sqrt computation and compare the squares instead.

using load/update Pixels generated the image a second faster than my old set(x,y,color(---)); which i don't really understand the difference. however, it now generates the image in about 3 seconds ..