But let's assume you have enough light that you're not seeing that nighttime monochrome effect...
In low light and shadow, you can have substantial changes from 5000K. this site seems to have a pretty good chart...
Some films will respond very poorly to deviations from 5000K. Others will do a bit better, but for the most part, if you really want to address this issue you need to get yourself a basic filter set and play around, and try some colour metering too if you can (n.b. a lot of digicams can act as colour meters and they are typically less expensive than a colour meter!).
Now, some films can handle mixed colour temps better than others. So as not to ruffle feathers, I won't mention specific brands that I didn't care for. There was one which reminded me of that terrible movie Ishtar. Anyway, I'll just say that I've had pretty good luck with fuji pro s and pro h in mixed / non-optimal light, and I thought reala was pretty good too.
The big problem with filtering is that it's very easy to overdo it. What drives me nuts is a landscape scene shot at sunrise or sunset which is nevertheless filtered to look like something else. One has to use restraint, of course!
And again, this is issue is quite separate from all the exposure stuff. Welll... okay, it's related in the sense that shooting colour film is kinda analogous to shooting several stacked, colour-filtered black & white films together, simultaneously. If you want to think that way, then to get the colours right, you will need to apply zone principles to expose each separate layer correctly. But the only sensible way to do that is to compensate for the colour temp as a whole. At least that way you aren't attempting to three or four coupled zone system problems
In other words, adjusting the overall exposure to all layers does not solve the problem of whether each layer is getting optimal exposure. That's why we filter.