A US pattern says “H hook”, your hook says 5mm, and a UK pattern calls it a 6. They're the same hook.
| Metric (mm) | US | UK |
|---|---|---|
| 2.0 | — | 14 |
| 2.25 | B/1 | 13 |
| 2.5 | — | 12 |
| 2.75 | C/2 | — |
| 3.0 | — | 11 |
| 3.25 | D/3 | 10 |
| 3.5 | E/4 | 9 |
| 3.75 | F/5 | — |
| 4.0 | G/6 | 8 |
| 4.5 | 7 | 7 |
| 5.0 | H/8 | 6 |
| 5.5 | I/9 | 5 |
| 6.0 | J/10 | 4 |
| 6.5 | K/10½ | 3 |
| 7.0 | — | 2 |
| 8.0 | L/11 | 0 |
| 9.0 | M-N/13 | 00 |
| 10.0 | N-P/15 | 000 |
| 11.5 | P/16 | — |
| 15.0 | P-Q | — |
| 16.0 | Q | — |
| 19.0 | S | — |
| Metric (mm) | US | UK |
|---|---|---|
| 2.0 | 0 | 14 |
| 2.25 | 1 | 13 |
| 2.75 | 2 | 12 |
| 3.0 | — | 11 |
| 3.25 | 3 | 10 |
| 3.5 | 4 | — |
| 3.75 | 5 | 9 |
| 4.0 | 6 | 8 |
| 4.5 | 7 | 7 |
| 5.0 | 8 | 6 |
| 5.5 | 9 | 5 |
| 6.0 | 10 | 4 |
| 6.5 | 10½ | 3 |
| 7.0 | — | 2 |
| 7.5 | — | 1 |
| 8.0 | 11 | 0 |
| 9.0 | 13 | 00 |
| 10.0 | 15 | 000 |
| 12.75 | 17 | — |
| 15.0 | 19 | — |
| 19.0 | 35 | — |
| 25.0 | 50 | — |
A dash means that system has no direct equivalent. US letter sizes vary a little between manufacturers, so when a pattern matters, go by the millimetres stamped on the hook — and swatch either way.