The algebra of the group R5 of rotations in 5-dimensional Euclidean space coincides with the symplectic algebra sp(4). The Casimir operators of sp(n), with n even, are C2, C4, ..., C2ν, where ν = n/2 and Cp is the invariant Casimir operator of order p, which can be explicitly calculated. For details, see Sections 1.15, p. 13, and 7.2.5, p. 95, of the excellent book Lie Algebras and Applications, 2nd edition, by Francesco Iachello (Springer, Berlin, 2015).