Here I combine Zucca's two problems and show compatibility figures for three pentominoes with an odd number of tiles!
His solution has 61 tiles! Smaller solutions have since been found. See the table below.
| 5F+5I+5L | 5F+5I+5N | 5F+5I+5P | 5F+5I+5T | 5F+5I+5U |
|---|---|---|---|---|
 23 | 
|  13 |
|
|
| 5F+5I+5V | 5F+5I+5W | 5F+5I+5X | 5F+5I+5Y | 5F+5I+5Z |
|
|
| 
|  21 |
|
| 5F+5L+5N | 5F+5L+5P | 5F+5L+5T | 5F+5L+5U | 5F+5L+5V |
 11 |  7 |  19 |
|  11 |
| 5F+5L+5W | 5F+5L+5X | 5F+5L+5Y | 5F+5L+5Z | 5F+5N+5P |
 15 |
|  7 |  23 |  5 |
| 5F+5N+5T | 5F+5N+5U | 5F+5N+5V | 5F+5N+5W | 5F+5N+5X |
 25 |  27 |  15 |  9 |  33 |
| 5F+5N+5Y | 5F+5N+5Z | 5F+5P+5T | 5F+5P+5U | 5F+5P+5V |
 7 |  13 |  11 |  17 |  9 |
| 5F+5P+5W | 5F+5P+5X | 5F+5P+5Y | 5F+5P+5Z | 5F+5T+5U |
 7 |  19 |  7 |  13 | |
| 5F+5T+5V | 5F+5T+5W | 5F+5T+5X | 5F+5T+5Y | 5F+5T+5Z |
|
|
|
|  13 | |
| 5F+5U+5V | 5F+5U+5W | 5F+5U+5X | 5F+5U+5Y | 5F+5U+5Z |
|
|  21 |
|
|
|
| 5F+5V+5W | 5F+5V+5X | 5F+5V+5Y | 5F+5V+5Z | 5F+5W+5X |
|
|
|
|
|
|
| 5F+5W+5Y | 5F+5W+5Z | 5F+5X+5Y | 5F+5X+5Z | 5F+5Y+5Z |
 13 |
|  17 |
|  21 |
| 5I+5L+5N | 5I+5L+5P | 5I+5L+5T | 5I+5L+5U | 5I+5L+5V |
|
|  7 |
|
|
|
| 5I+5L+5W | 5I+5L+5X | 5I+5L+5Y | 5I+5L+5Z | 5I+5N+5P |
|
|
|  11 |
|  11 |
| 5I+5N+5T | 5I+5N+5U | 5I+5N+5V | 5I+5N+5W | 5I+5N+5X |
|
|
|
|
|
|
| 5I+5N+5Y | 5I+5N+5Z | 5I+5P+5T | 5I+5P+5U | 5I+5P+5V |
 13 |
|
|
|  29 |
| 5I+5P+5W | 5I+5P+5X | 5I+5P+5Y | 5I+5P+5Z | 5I+5T+5U |
 17 |
|  9 |
|
|
| 5I+5T+5V | 5I+5T+5W | 5I+5T+5X | 5I+5T+5Y | 5I+5T+5Z |
|
|
|
|
|
|
| 5I+5U+5V | 5I+5U+5W | 5I+5U+5X | 5I+5U+5Y | 5I+5U+5Z |
|
|
|
|
|
|
| 5I+5V+5W | 5I+5V+5X | 5I+5V+5Y | 5I+5V+5Z | 5I+5W+5X |
|
|
|
|
|
|
| 5I+5W+5Y | 5I+5W+5Z | 5I+5X+5Y | 5I+5X+5Z | 5I+5Y+5Z |
 29 |
|
|
|
|
| 5L+5N+5P | 5L+5N+5T | 5L+5N+5U | 5L+5N+5V | 5L+5N+5W |
 5 |  35 |
|  13 |  11 |
| 5L+5N+5X | 5L+5N+5Y | 5L+5N+5Z | 5L+5P+5T | 5L+5P+5U |
|
|  19 |
|  13 |  13 |
| 5L+5P+5V | 5L+5P+5W | 5L+5P+5X | 5L+5P+5Y | 5L+5P+5Z |
 7 |  7 |
|  7 |  23 |
| 5L+5T+5U | 5L+5T+5V | 5L+5T+5W | 5L+5T+5X | 5L+5T+5Y |
|
|  15 |
|
|  15 |
| 5L+5T+5Z | 5L+5U+5V | 5L+5U+5W | 5L+5U+5X | 5L+5U+5Y |
|
|
|
|
|
|
| 5L+5U+5Z | 5L+5V+5W | 5L+5V+5X | 5L+5V+5Y | 5L+5V+5Z |
|
|  23 |
|  19 |
|
| 5L+5W+5X | 5L+5W+5Y | 5L+5W+5Z | 5L+5X+5Y | 5L+5X+5Z |
|
|  13 |
|
|
|
| 5L+5Y+5Z | 5N+5P+5T | 5N+5P+5U | 5N+5P+5V | 5N+5P+5W |
 19 |  23 |  15 |  19 |  7 |
| 5N+5P+5X | 5N+5P+5Y | 5N+5P+5Z | 5N+5T+5U | 5N+5T+5V |
 33 |  7 |  21 |
|
|
| 5N+5T+5W | 5N+5T+5X | 5N+5T+5Y | 5N+5T+5Z | 5N+5U+5V |
|
|
|
|
|
|
| 5N+5U+5W | 5N+5U+5X | 5N+5U+5Y | 5N+5U+5Z | 5N+5V+5W |
|
|
|
|
|
|
| 5N+5V+5X | 5N+5V+5Y | 5N+5V+5Z | 5N+5W+5X | 5N+5W+5Y |
|
|
| |
|
| 5N+5W+5Z | 5N+5X+5Y | 5N+5X+5Z | 5N+5Y+5Z | 5P+5T+5U |
|
|
| |
 51 |
|
| 5P+5T+5V | 5P+5T+5W | 5P+5T+5X | 5P+5T+5Y | 5P+5T+5Z |
 15 |
|
|  19 |
|
| 5P+5U+5V | 5P+5U+5W | 5P+5U+5X | 5P+5U+5Y | 5P+5U+5Z |
|
|  19 | |
|
|
| 5P+5V+5W | 5P+5V+5X | 5P+5V+5Y | 5P+5V+5Z | 5P+5W+5X |
 21 | |
 19 |
|
|
| 5P+5W+5Y | 5P+5W+5Z | 5P+5X+5Y | 5P+5X+5Z | 5P+5Y+5Z |
 11 |  15 |  29 | |
 11 |
| 5T+5U+5V | 5T+5U+5W | 5T+5U+5X | 5T+5U+5Y | 5T+5U+5Z |
|
|
|
|
|
|
| 5T+5V+5W | 5T+5V+5X | 5T+5V+5Y | 5T+5V+5Z | 5T+5W+5X |
|
|
|
|
|
|
| 5T+5W+5Y | 5T+5W+5Z | 5T+5X+5Y | 5T+5X+5Z | 5T+5Y+5Z |
|
|
|
|
|
|
| 5U+5V+5W | 5U+5V+5X | 5U+5V+5Y | 5U+5V+5Z | 5U+5W+5X |
|
|
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|
|
| 5U+5W+5Y | 5U+5W+5Z | 5U+5X+5Y | 5U+5X+5Z | 5U+5Y+5Z |
|
|
|
|
|
|
| 5V+5W+5X | 5V+5W+5Y | 5V+5W+5Z | 5V+5X+5Y | 5V+5X+5Z |
|
|
| |
|
| 5V+5Y+5Z | 5W+5X+5Y | 5W+5X+5Z | 5W+5Y+5Z | 5X+5Y+5Z |
|
| |
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Last updated 2017-08-26.