Does the lighting to my plants suffice all of their needs?

This is the first time growing for me. Due to a lack of places where I could
purchase equipment, I aquire some Light of America under cabinet lights
http://www.lightsofamerica.com/Products/7020.aspx . I currently
employ five of them in a space that is 1yrd x 19inch. Is my light setup
enough for my plants to suffice their needs?

You might be able to veg a lil under those.. cfls would do better if you cant find anything else.

you have no where near enough light. A rough rule of thumb is 50 watts of high output lighting per square foot. you have 4.75 ft, you need 237 watts of light for that space. thats like 14 of the 17 watt t8 flouros that you have. alot of people will tell you to mail order 250 watt hps light, but you can buy smaller ones, like 100 watters at home depot and lowes, they are outdoor secuity lights. the you could also buy some compact florescents, they sell them everywhere, like the grocery store. I would add like 8 23 watt cfls. 23 watts is the most common size, they call they 100 watt equivalents, dont be fooled they are 23 watts. your lights you have now are 17 watts, not 75 like it says. florescent lights are way more effeicient than regular incandescent light bulbs, so they put the incandescent wattage equivalent on the package some times bigger than the actual wattage. look at some threads on here about lst and scrog methods of growing if you want to stick with the flouros, check out the cfl section too. good luck with your first grow. its awesome to be self sufficient for buds.

^Agreed. You can use them for the first 18 hours, that's about it.lol If you want to have enough light, for certain, go with two 150-175 watt HPS lights. Those'll get you some really nice bud. You could go with CFLs if you wanted, but you'll have alot of trouble competing with that HPS setup, especially at harvest-time. VERY FEW growers manage to get buds that are near the density that HPS can grow. The HPS is much easier to setup and get great results. One 400 watt light would work too, but wouldn't fit the area as nice as the 175's.

so if i were to run my current setup plus the 8 23 watt cfls, i would be fine? and what if i were to cut back in space 50%?

dont cut back on your space, if you have it, use it. if you add the cfls you will be able to grow some decent buds with that much light.
just keep them very close to your plants, like 2-3 inches away, and i would highly recomend the scrog method

i was thinking os starting to LST myplants, what do you think?

lst is a cool method too, i think the trick to growing with flouros is to have a very even canopy, so you can keep the lights really close.