  An algebraic classification of second order symmetric tensors in
5-dimensional Kaluza-Klein-type Lorentzian spaces is presented by using Jordan
matrices. We show that the possible Segre types are $[1,1111]$, [2111], [311],
[z,\bar{z},111], and the degeneracies thereof. A set of canonical forms for
each Segre type is found. The possible continuous groups of symmetry for each
canonical form are also studied.
