New radio observations of the counterpart of the ultraluminous X-ray source in NGC 5408 show for the first time that the radio emission is resolved with an angular size of 1.5 \arcsec to 2.0 \arcsec . This corresponds to a physical size of 35–46 pc , and rules out interpretation of the radio emission as beamed emission from a relativistic jet . In addition , the radio spectral index of the counterpart is well determined from three frequencies and found to be \alpha = - 0.8 \pm 0.2 . The radio emission is likely to be optically-thin synchrotron emission from a nebula surrounding the X-ray source . The radio luminosity of the counterpart is 3.8 \times 10 ^ { 34 } erg s ^ { -1 } and the minimum energy required to power the nebula is \sim 1 \times 10 ^ { 49 } erg . These values are two orders of magnitude larger than in any Galactic nebula powered by an accreting compact object .