Why are my cucumber seedlings so lanky?

I planted cucumber seeds {burpless and straight 8's} 2 weeks ago in the 3" peat pots that you can purchase at WalMart ect. and they were getting so lanky and toppling over so this weekend I transplanted them in tall 6 to 8"plastic McDonald cups with hole in bottom for drainage and they are starting to droop again. I keep them well watered and they are still inside my home with 5 hours of light daily. We're having a late frost Tues. night and my garden is not ready to transplant these seedlings. Should I just scrap all of these seedlings and start over in a week or 2 when my garden is ready or will they be ok? They are green and heathy looking and I thinned them down to one strong plant per cup. When I transplanted to the larger cups should I have gone up to the leaf with the new soil? I just transplanted the way they were in the smaller pots. Should I add more dirt ? See photos.
Any suggestions are sincerly appreciated. Thanks for your time and have a nice week.
I also placed this question in beginner vegetable forum.

How close are your lights to the plants? If they're more than a few inches above the seedlings, they're really not doing you much good. They also need LOTS more than 5 hrs of light daily, when I have seedlings I leave the lights on for 16 hours. You probably don't need to scrap them--fix the light situation for now, and when you transplant them into the garden many seedlings can be planted deeply, up to the first set of leaves, so that can get rid of the initial legginess.

I just have overhead lights and they are far away from the plants. I'll set a lamp up near them and leave the light on for many more hours as you suggested. Thanks so very much for the quick response.

Cucumbers sprout and grow so quickly that I'd wait and direct sow them. The ones you have there are not getting enough light. If you direct sow, they will come up much stronger than what you have there.

Thanks naturelover. Think I'll just scrap the whole project and start over directly into the garden when dry enough to til.
Have a nice evening.

mine looked the same--i had 2 in with my tomatoes which also look the same--i put dirt up to the leaves and am hoping they do better now--

I put them outside next to the steps and we had a light frost this morning but they didn't die. It's almost like they knew I was going to trash them and they decided to wake up. They're all perky now so I think I'll do like you did and just add more dirt and hope for the best. They may be my best cucumbers this season; who knows? Can't give up on them yet. I had them in the house and now they're ouside so maybe that's all they wanted was a little fresh air and sunshine. I may have been giving them too much attention in the house. I'll just ignore them and see what happens. lol
Good luck with yours.

thanks--mine haven't perked up but haven't died either!

Not enough light. They're stretching for more light in that photo. Light(s) should be a few inches above top of soil. For about 14 hours a day.

I start cucumbers inside, but just a couple of weeks before planting them out so they're not too big.

I agree that light is the issue. Putting them outside on any mild day is fine, but they can get shocked by sudden exposure to sun, wind, etc... gradually acclimating seedlings to outside conditions is known as "hardening off" and is generally recommended. But it sounds like you've got some tough little cukes on your hands!

Here's an article I wrote on lights for starting seeds indoors: http://davesgarden.com/guides/articles/view/464/