The saber ist of the Prussian M 1816 pattern, which was identical to the French saber of the 1803 pattern. In 1814 and 1815 many French sabers had been taken from French depots by the Prussian army, that it was the cheapest solution to introduce this pattern officially.
The Prussian 37. Infanterie-Regiment (5. Reserve-Regiment) was created in 1820. It was renamed Westfälisches Füsilier-Regiment Nr. 37 in 1860.
The addition "5. Reserve-Regiment" was sometimes omitted, see link below.
Thus, ther saber can be dated between 1820 and 1860.