P90X weights?

When I was doing P90x the only weights I had were 2x1.5kg, 2x2.5kg, and 2x5kg. They worked just fine, since I usually did 8-12 reps compared to 3-8 on my heavy lifting at the gym. And P90x does tire you out, you don't get as long rests between sets and IMO you can lift nothing like what you can at the gym.
Since you're not used to heavy lifting they should definitely be fine for you, unless you're super naturally strong Although I would get a 2nd 5kg dumbell just so you can use 1 on each side. I doubt you'll need anything less than 5kg for the big movements such as deadlifts/squats.

I usually use the 5's for shoulder press type moves, any deadlift/squat movements, rows, that sort of thing. I also use them for the first set or two of bicep curls but then usually switch to 2.5kg. Most of the other stuff is 2.5kg, apart from half the tricep stuff I might use 1.5, and the shoulder exercises where you bring them out ahead of you and to the side I use 1.5 as they get you doing 16 reps and it's exhausting! They also do those shoulder circle movements where it's like you're swimming with both arms at once, usually I don't even use a weight for that, it's so hard!