When and why did 5.8 GHz become an ISM band?
After quite an exhaustive search, I have been unable to determine when the 5.8 GHz ISM band was initially allocated.  Although one document implies it was done in 1947 along with the 2.45 GHz ISM band, the ITU document you referenced makes it pretty clear the only ISM bands allocated back then were 13.66 MHz, 27.320 MHz, 40.980 MHz, and 2.45 GHz as you stated.

In 1985, the 2.45 GHz ISM band was opened up to general communication, but requiring the use of spread spectrum techniques to reduce interference from other activities on the band.
In 1997, the same thing was done for the 5.8 GHz ISM band, due to the potential for severe RF congestion in the 2.4 GHz band.

So the 5.8 GHz ISM band was initially allocated sometime in the 50 year span between 1947 and 1997.  Not very precise, sorry.

In the 5.8 GHz band, 5.725–5.875 GHz is specifically allocated to ISM and also used for wireless LAN (802.11/a).

BTW you wouldn't want to use the 4.9 GHz, as you wouldn't want to use a band that is the second harmonic of devices in the the busy 2.45 GHz (although all devices must be tested that they produce no harmful emissions for FCC certification, so there should  theoretically be no interference).

Besides avoiding congestion in the 2.45 GHz band, using the 5.8 GHz band allows for higher data rates.

However operating in a higher frequency band increases the noise level, obstacles and walls are more opaque to transmissions and a higher bit rate requires more SNR (Signal Noise Ratio), which means a reduced range compared to 2.4 GHz products.

Some of the products that specifically make use of the 5.8 GHz band are baby monitors, cordless phones, and cameras (mentioned, for example, here and several other documents).  It's not clear to me whether cordless telephones should be classified as ISM or communications -- I guess it depends on whether they use spread spectrum or not.

I also found this digital microwave radio that has a bandwidth of 39 MHz and a range of 45 Km.  It is a wireless extension of a STM-1 fiber optic network.  So this would definitely be an ISM application.

Research in using RFID technology in the 5.8 GHz ISM band is being carried out also.