I handle tons of C300 mk1 50Mbps material at work and it usually looks fine when graded properly, even for 2k DCP output on big screen, but the codec is very bad and blocky when underexposed so you have to be extremely careful in low light. definitely take something with a higher bitrate, preferably prores or raw if possible.
The F5 is a lot better camera than FS7 and depending on the specific FS7 body there may be a huge difference in noise levels, even something like double the noise on FS7 compared to F5.
the FS7 is otherwise quite handy camera, just don't expect it to go any further than about ISO 1000 in low light. But if you can get a raw capable external recorder to it like Atomos or 7Q+ then it might be quite good choice, then you could take it a little further because you wouldn't need to worry about underexposing slog which may look bad in some situations.
if you are on a budget I would maybe take the A7S2 for the low light capabilities. but as Tyler said it is in any case much better to have some additional light in the first place so that you can control the shadow detail and also won't have as much problems with the huge contrast between flames and shadow areas which is hard for any camera, especially when dealing with low color temperature (very underexposed warm shadow areas --->huge underexposing of the blue channel---> very noisy and blocky blue channel which is very difficult to restore and needs lots of noise reduction and dealing with the compression artifacts, to the extent of having completely unusable blue channel which you have to blur to get usable image)