growth rates vary but 5" at 4 months is not good at all. There are 2 things that determine size. #1 is genes. good genes allow BDs to grow to their normal size of 16-24". In order for them to meet their potential however they have to have good husbandry (and let me emphasize every BD is different but there are some basic points that are the same)
1) if you have not heard it before, you should not have been sold a BD that small. It should have been 6" when you bought it. that gives your BD the best chance of survival.
2)baby BDs need heat of up to 115F to properly digest food, 12 hours a day. your cool side is fine.
3) they need proper nutrition, a diet VERY HIGH in protein (plant or animal).
4) while some will argue about UV light, let me say IT CAN'T hurt. Spend the money and get it especially if there is a problem. make sure it is a good one and make sure you use it correctly or it does no good.
5) Supplement properly I had some non growers that got on T-Rex VGF and it did help. I also have some that it did not help, but they have other problems.
6) yes those parasites are a problem and can lead to a vicious downward spiral if not kept in check
I can see that you are trying so even though you posted some info, you need to answer some more questions.
There are basic husbandry techniques that if not followed can cause a myriad of problems. In order to give you an answer based on fact and knowledge, you need to answer some basic questions.
How long have you had your BD?
How long have you had this problem?
Where did you get your BD (breeder, pet store, rescue…)?
How old is your BD?
How big is your BD (length, weight)?
How big is the enclosure?
What are the temps?
What type of lighting do you use?
What is the substrate?
What is your BDs diet? Be detailed here, type and size of food.
DO you supplement? If so what and how often?
When was your BDs last fecal?
Answering these questions is a good starting point. Anytime you have a question about the health of your animal, this info should be included so you can get educated answers not a blind guess.
It may help if you read this care sheet
BD Q&A
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Bennett

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