ergo exergy ucg technology agreement..., page-8

It's pretty easy, mate, one Watt (W) is equal to 1 Joule per second (J/s), so for 5PJ per annum:

5PJ = 5 billion MJ
31.5 million seconds in a year

So 5PJ/yr = 160MW gross. At efficiency of about 30% that's about a 50MW power plant.

Carbon Energy's figure is a little high, it assumes an efficiency of 50-65%. They might have another step in there to increase efficiency, or they might already be taking some loss of efficiency into account when they calculate their 1PJ of syngas.

Whichever it is, the two figures are in the same ballpark.