Hi,
On Ancestry under UK, Naval Officer and Rating Service Records, 1802-1919 you can see
Information re ships on which he served.
Mathew Hambley, Liskard
Port Royal 24.7.1803 to 16.6.1804
There is then a note :- as Hennly? Hard to read, but different spelling of his surname.
And at the Battle of Trafalger
Belleisle 16.6.1804 to 9.1.06
The list goes on ending 31.8.1814
If you do not have Ancestry, it may be possible to access via your local library.
For information on the ship Belleisle:-
https://en.m.wikipedia.org/wiki/HMS_Belleisle_(1795)
And a good painting on
https://www.pinterest.co.uk/pin/774337729654211533/His service commenced in 1803 when he was aged 20 years, so born 1783.
Regards Spendlove