We have a package with 5 live streaming channels. Is there a way to have 2 different, but simultaneous live streams embedded to 2 different websites, or must all 5 live channels have the same content?

Absolutely. The live streaming channels can be adjusted and used in any way you need them. E.g. to set up and stream with different bandwidth (HQ, MQ, LQ - one quality per channel) or to use them for simulated live as you mentioned. Yes, you can use 2 different live channels for 2 different simultaneous live streams. For each of the live channels there is an embed code which you can use to embed on different websites. The 5 live channels don't need to stream the same content.