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Just as a side note: lumens is how we see the light (visible spectrum) but not necessarily as helpful to the plants. PAR or PUR are more appropriate for plants. PAR (photosynthetically available radiation) or PUR (photosynthetically useful radiation). Some lights have ratings for one of these as they are far more common and accurate to the needs of aquarist gardeners than any other measure.
Probably. The 5000K is OK, it is "warmer" in terms of light which means more red and less blue ("cool" means more blue and less red), and red is important for photosynthesis, so that is not a problem.