It appears that the satellite has indeed been transmitting recently; here's a video with evidence of signal reception in 2014. I don't know enough about software-defined radio to understand exactly what's going on there but something seems to be signaling.
Regarding power supply, I don't have any authoritative sources, but the Transit page on wikipedia mentions some of the Transit sats having RTGs/"nuclear power sources". 5B5 isn't among them:
- Transit 4A, launched June 29, 1961, was the first satellite to use a radioactive power source (RTG) (a SNAP-3). Transit 4B (1961) also had a SNAP-3 RTG. ...
- Transit 5A3 and Transit 5B-1 (1963) each had a SNAP-3 RTG.
- Transit 5B-2 (1963) had a SNAP-9A RTG.
- Transit-9 and 5B4 (1964) and Transit-5B7 and 5B6 (1965) each had "a nuclear power source".
Note that the illustration on the page shows solar panels but doesn't specify which satellite it is.
The SNAP page, however, gives us a big hint:
After SNAP-3 on Transit 4A/B, SNAP-9A units served aboard many of the Transit satellite series. In April 1964 a SNAP-9A failed to achieve orbit and disintegrated, dispersing roughly 1 kilogram (2.2 lb) of plutonium-238 over all continents. Most plutonium fell in the southern hemisphere. Estimated 6300GBq or 2100 man-Sv of radiation was released and led to NASA's development of solar photovoltaic energy technology.
Astronautix says:
There were three series of operational prototypes to finalize other design choices. The Transit 5A and 5C-1 prototypes used solar power, and the 5BN series used nuclear power. The 5E series used solar power but instead of the navigation package had instruments to measure the Transit orbital environment. To accomplish this they were launched piggy-back with the 5B series using Thor Able-Star boosters.
After the failure of Transit 5BN-3 to achieve orbit, it was decided that operational satellites would be solar powered. Not only was the cost lower, but the need to obtain special approvals to launch each nuclear-powered satellite and the operational and publicity issues in case of a failure to orbit were unacceptable.
So it seems that 5B5 was redesigned for solar power after the accident.