It is difficult to know for sure, but it is likely that you couldn't discern color well, if at all.
The only reference we get to the working of dim light comes from this excerpt in the Player's Handbook:
Dim light, also called shadows, creates a lightly obscured area. An area of dim light is usually a boundary between a source of bright light, such as a torch, and surrounding darkness. The soft light of twilight and dawn also counts as dim light. A particularly brilliant full moon might bathe the land in dim light.
Using the few explicit examples of dim light we have, twilight, dawn, and moonlight provide much less light than the sun, and it would therefore be more difficult to make out color (except perhaps bright reds and blues).
While we can't extend the real world directly into the game world, it is a good starting point. Next we have to work with the "lightly obscured area" bit.
In a lightly obscured area, such as dim light, ... creatures have disadvantage on Wisdom (Perception) checks that rely on sight.
Extrapolating from the Ability Check system
Identifying color would, fundamentally, be a Wisdom (Perception) check of very low DC (while in bright light at least):
[Perception] measures your general awareness of your surroundings and the keenness of your senses
but in dim light that DC may change as it could be classed as a Hard or Very Hard task (as assumed from the examples of what constitutes dim light) and you would have disadvantage due to the light obscurement:
The more difficult a task, the higher its DC.
Essentially, since the light is dim and therefore lightly obscured, identifying color moves from a DC 0-5 perception check (which is easily covered by anyone's Passive Perception) to a DC 20-25 with disadvantage.
TL;DR: Identifying color in dim light requires exceptionally high Perception or reasonably high Perception and active focus on the object/area whose color you are trying to identify.