Fly into Vientiane. Spend the next day doing sightseeing. Fly to Luang Prabang, spend 3 days there. Fly back to Vientiane and spend your penultimate day there doing more sightseeing.
The cheapest flight option Bkk to Lao is Nok Air or Air Asia booked online in advance to Udon thani, one hour from the lao border or 90 mins- 2 hrs from vientiane.
Alternatively there is a clean comfy night sleeper train leaving Bkk every evening, getting to lao border at nong khai early every morning.
I'm taking the train to Nong Khai and rail connection into Vientaine, spend 4 days there and a Lao flight to Luang Prabang. 4 more days in Luang Prabang and then on to Hanoi with Lao Airlines again. Be sure to book online for cheaper fares.
I would think with only 5 days, that Luang Prabang would be your main center of interest. You can fly directly there with either Lao Airlines or Bangkok Airways - similar service (Lao slightly cheaper).
I agree with one of the posts that says that with only 5 days you should concentrate on Luang Prabang. Me and my husband flew from BKK directly to Luang Prabang with Lao Airlines. We bought the tickets at their office in Suvarnabhumi Airport, because we could not do it through the internet. However, we paid exactly the same price.
Spent 6 nights, 5 days there. The city is very nice, and there´s lot of things to see including temples, waterfall, elephant rides, boat tours. I have made some reviews on hotels and restaurants for trip advisor on the city. Regarding airlines, a dear thai friend whom I visited in BKK recommended me not to use Nok Air due to maintenance concerns.
5 days could very easily be spent in Luang Prabang (direct flights to Bangkok). Alternatively you could also spend a day in Vientiane as well. Flights from Bangkok are regular from Luang Prabang and Vientiane.
I would fly directly to Vientiane, spend a day or so there and then fly to Luang Prabang for the rest of the time. This option, while expensive, will at least give you a taster.
Didn't see Maneki's post. This is by far the most sensible opton. You won't waste time getting from Udon Thani to Vientiane and you will maximise your time.
I enjoy Luang Prabang's elephants, night market, bicycle tour and nice food...
Vientiane may be bit quiet for your daughter... Laos air is efficient but the return from Luang Prabang to Bangkok's bit early (07:35)
bangkok airways was good. their return from lp to bangkok is at 12 noon.