Landsat 5 DN's to Top of Atmosphere reflectance
Short answer: yes.

The Radiance to Reflectance correction described in the Handbook is just physics based. Therefore, it is valid for any Earth observing satellite. However, the mean solar exo-atmospheric irradiances (table 5-2) are specific to the wavelength bands of the ETM+ sensor. Therefore, if you want to correct other bands you would need new coefficients valid for the corresponding wavelength range.

But in the case of Landsat 5 and 7, the bands are almost identical (with very small differences on bands 4 and 7). Therefore, unless you need very high accuracy I would say that it is safe to use ETM+ coefficient (Landsat 7) to correct TM imagery (Landsat 4 and 5).

The bands for TM and ETM+ are as follows:





(taken from USGS Landsat Mission)

Note that it is not only the boundaries of the bands what matter, but also the spectral response within the band. Therefore, even for bands that seem identical, the coefficients of exo-atmospheric irradiances can present small differences.
Ideally, you should use the coefficients calculated specifically for the TM sensor, but using the ETM+ values would provide a very good approximation. At least good enough for most applications. But if you want to use the TM specific values, they are as follows:



(Taken from USGS Q&amp;A "Where can I find the solar exoatmospheric spectral irradiances (ESUN) for the Landsat 1-5 MSS, Landsat 4-5 TM, and Landsat 7 ETM+ sensors?")