It's not that putting it directly in a large pot is wrong per se. It's more difficult to maintain germination conditions for a large pot than a small one, and until the plant has a rootzone big enough to fill the pot you need to make sure things remain slightly on the drier side of indoors at least untill she has a solid rootzone filling inside of that 5 gallon, normally I find 5 gallons to be quite tall when you have a tiny seedling in a 5 gal in new tent the light can quickly evaporate top couple inches through evaporation, gravity will pull water out of reach of the tiny seedling quite fast so make sure to keep an vigilant eye. Good watering practice, you wanna fully saturate the soil with a little run off.
I'd suggest you buy yourself a soil EC meter, a solid one that costs 30-60 bucks. Then, just water water water until EC tells you to fertilize, then water water water. Keep range 0.5-1.8 never higher than 2