The projectile body of the 5cm Pzgr (V) is 161.2 mm long , the body of the Pzgr 39 –without piercing cap- is 152mm long.
German 37mm AP-shells did not have cap, but some German made for Czech 37mm did have.
As the projectile is unfired the piercing cap cannot have gone missing due to impact. It is tin brassed to the nose of the projectile and cannot be removed without extreme mechanical force. It can be removed by only heating up the projectile about 250 degrees so the tin brass melts away and the cap can be removed.