I want to know if I have the best way to combine 5 sentences.
1. This waste poses a threat to civilization.
2. This waste poses a threat to the environment.
3. The threat is extraordinarily serious.
4. Its radiation is so lethal.
5. Its radiation is so long-lasting.
My answer is
Because this waste's radiation is so lethal and long-lasting, it poses an extraordinarily serious threat to civilization and the environment.
Once again, your sentence is "correct," and also make use of formal grammar and sentence structure. However, you might want to "mix things up a bit," so that your sentences don't sound too similar in structure, which might occur if this is a pattern that you repeat.
By changing the structure of your sentence—the order in which you place its various elements—your writing can sound more interesting. This is especially true if you are completing this for a class where the sentence is going to be one of many read. Yours may end up sounding like all the other sentences; however, as you become a stronger writer, you will want to make your work stand out. This is something that will serve with college application letters and essays, as well as the pursuit of employment prospects.
A perfect example of more sophisticated writing can be seen with the simplicity of nursery rhymes, such as "Mary had a little lamb," or first grade readers that use "subject+verb" sentence structures, such as, "I see the apple." When you see this kind of writing, you recognize that your own writing is far more sophisticated. However, it making it more interesting, you don't want your writing to be difficult to understand, but simply more engaging.
I would first offer some context here, and then experiment with the order of the sentence. (And don't be afraid to use commas as necessary, as well as semicolons or colons.)
Waste is a necessary by-product of any civilization, but correct processing of it is an extraordinarily serious concern; it is imperative to avoid a potential threat to the environment—as seen with the long-lasting and lethal effects of radiation.
One thing to try to do when joining these related ideas is to avoid using a word repeatedly. You have already done this by using "pose" only once, though it appears in two sentences. You have done the same with "Its radition is so…" Repeating these words or phrases would make the writing sound monotonous; at the same time, this repetition in your basic sentences also points to the relationship between these items and helps you to find elements that can be combined in your final sentence. I took out "poses" and wrote about "avoiding a potential threat." The content is the same: the information you have highlighted is included. My suggestion looks at the information in a slightly different way without losing the central meaning of the information.
Your sentence is absolutely correct: there is no question—it is nicely done. At some point you might want to try to experiment with switching the word order (syntax), and/or the sentence structure to find a different "sound" for your writing.