Polarized and unpolarized neutron inelastic scattering has been used to measure the spin excitations in the spin-charge-ordered stripe phase of La5/3Sr1/3NiO4. At high energies, sharp magnetic modes are observed characteristic of a static stripe lattice. The energy spectrum is described well by a linear spin wave model with intra- and inter-stripe exchange interactions between neighbouring Ni spins given by J = 15 +/- 1.5 meV and J = 7.5 +/- 1.5 meV respectively. A pronounced broadening of the magnetic fluctuations in a band between 10 meV and 25 meV is suggestive of coupling to collective motions of the stripe domain walls.
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