We present results from a comprehensive survey of 70 radio galaxies at redshifts 1 < z < 5.2 using the PACS and SPIRE instruments on board the Herschel Space Observatory. Combined with existing mid-IR photometry from the Spitzer Space Telescope, published 870 µm photometry, and new observations obtained with LABOCA on the APEX telescope, the spectral energy distributions (SEDs) of galaxies in our sample are continuously covered across 3.6-870 µm. The total 8-1000 µm restframe infrared luminosities of these radio galaxies are such that almost all of them are either ultra-(L IR tot > 10 12 L ) or hyper-luminous (L IR tot > 10 13 L ) infrared galaxies. We fit the infrared SEDs with a set of empirical templates which represent dust heated by a variety of starbursts (SB) and by an active galactic nucleus (AGN). We find that the SEDs of radio galaxies require the dust to be heated by both AGN and SB, but the luminosities of these two components are not strongly correlated. Assuming empirical relations and simple physical assumptions, we calculate the star formation rate (SFR), the black hole mass accretion rate (Ṁ BH ), and the black hole mass (M BH ) for each radio galaxy. We find that the host galaxies and their black holes are growing extremely rapidly, having SFR ≈ 100-5000 M yr −1 anḋ M BH ≈ 1-100 M yr −1 . The mean specific SFRs (sSFR) of radio galaxies at z > 2.5 are higher than the sSFR of typical star forming galaxies over the same redshift range, but are similar or perhaps lower than the galaxy population for radio galaxies at z < 2.5. By comparing the sSFR and the specificṀ BH (sṀ BH ), we conclude that black holes in radio loud AGN are already, or soon will be, overly massive compared to their host galaxies in terms of expectations from the local M BH -M Gal relation. In order to catch up with the black hole, the galaxies require about an order of magnitude more time to grow in mass at the observed SFRs compared to the time the black hole is actively accreting. However, during the current cycle of activity, we argue that this catching up is likely to be difficult because of the short gas depletion times. Finally, we speculate on how the host galaxies might grow sufficiently in stellar mass to ultimately fall onto the local M BH -M Gal relation.