Sluggish new betta fish!

Question
QUESTION: My betta is one week old, and was doing fantastic in his 1 gallon tank.  I did a bunch of research and decided the tank was too small. (it did have a filter and a heater) So, I purchased a 5 gallon tank, treated the water, added a filter and heater, let it set for 2 hours, and added my betta. The next day he was extremely lethargic and so listless.  I believe I added him too quickly to this new environment.
So, what do I do now?  I changed out 10% of the water (due to the fact that I had added some mondo plants too), threw them out after reading they too are bad!  Now I wish I had just left things alone in his little "efficiency apartment"!

I think/hope he will recover, but how long should I wait before trying something else?  
Thanks so much! I enjoy him so much; this is my first betta/tank!

ANSWER: Bev,
Is he one week old, or have you had him for one week? The 5 gallon tank is great, just remove the filter. The male Betta does not like nor does he need a filter. When you have filter, you have to cycle it before you add the fish. This is a 6 week process, sometimes longer.I do not think he is ill but might be reacting to the water being too cold. He needs his water to be at 80 degrees at all times. It takes awhile for the heater to warm up the water. Once his water is 80 degrees, he should be just fine.

---------- FOLLOW-UP ----------

QUESTION: Thanks so much for your reply!  Guess what? This morning Eve (I got him on Christmas Eve) is better! I put him back in the 1 gallon tank (yes, I know he "needs" 5 gallons, but it about killed him in my mind!!)...should I turn off the filter in the one gallon tank based on what you said above?

And I've owned him for a week, he's however old he was when we purchased him from Pet Smart.

So much information out there, it gets confusing!  
Also, his fins aren't as open as they were before he went into "shock"...will they come back, do you think?
Thanks again!!

ANSWER: Since he is back in the small tank, yes turn off the filter. It would be in his best interest to be placed back into the larger tank. Keep the heater going in the 5 gallon. It take approx. 48 hours for the heater to get to the 80 degrees and maintain it. Make sure you have a thermometer in the tank so you can be sure it is the right temp. Once it hits 80 degrees, put him back in the 5 gallon. He is now showing clamped fin because of all the moving he has been doing. It is best for these guys to get into the right home to start and then stay in it. If you keep him in the 1 gallon tank you will not only cut his life spam down, but will start having other issues. You can dissolve 1/2 teaspoon of aquarium salt and add is to his water during a water change. This is the only thing I use for mine.

---------- FOLLOW-UP ----------

QUESTION: Well, now I'm just plain scared to transfer Eve again. I think I'll wait a couple of weeks, don't you think?  My thought there is it gives him plenty of recovery time. I did turn the filter off, and will keep it off at this point. But I will say, with the filter the water looked so much clearer. :)

How often should I change the water in the 1 gallon?  Do you think a 25% partial change once a week is ok?  And when I do this, I'm de-clorinating the water before adding it, should it  set out for a couple of hours?  If that's the case, it gets kind of cold (I do live in Alaska!)....but being only 25% and added slowly, is this ok?

so many questions!  Again, thank you so much!

Answer
In the 1 gallon tank, the water changes have to be done more often. Do 25% changes every 2-3 days. Keep in mind, fish do stress a little during a water change. With you having to do it more often, keep a close eye on him that it doesn't stress him too much. The sooner you can get him into the 5 gallon tank the better off he will be.