Popular misconception: sore isn't really the determining factor for how much weight to lift or whether you had a good workout. Some people never get sore, some only get sore sometimes, some people get sore the next day. The test for weight is whether you can complete a full set while maintaining good form (like no back swaying on biceps curls) and yet it feels difficult. If doing that seems easy, then you can probably handle more weight.

If you go to a store like Walmart or Target, try out their dumbbells right there and you'll know what weight you can handle...but do a full set to be sure.

I don't know what weight you got, but I don't see any reason most people can't start with 5 lbs. I've only gotten lower weights for Pilates, which has some 2-lb. exercises in its standard repertoire.