Hi,
Next year, I will have been living here for 5 years.
Next year, I will have lived here for 5 years.
Is the second sentence more correct Both are OK and, if it isn't, is there a difference between the sentences? Yes
Let's consider these two simpler examples, that relate to the present rather than to the future. The principle is the same.
I have lived here for 5 years. As you know, this draws attention to a past period that has relevance to the present.
I have been living here for 5 years. Similar to the above, but stresses the duration, the length of the period, and often that the period has not been interrupted. The activity may be temporary, but not always. eg
A: Hello. I live down the street. I haven't seen you before. Did you just move into this house?
B: No, not at all, I've been living here for the past 5 years. I can't imagine why we've never met before.
I remember reading that 'living' is used only when it is temporary. As noted above, I wouldn't say it is always or only temporary.
eg I have been teaching English for 20 years does not seem temporary.
The perfect tenses can convey quite a range of meanings, and thus are difficult to learn. Do you have a good grammar book that deals with tenses? I recommend 'Teaching Tenses', by Rosemary Aitken, published by Thomas Nelson Ltd.
Best wishes, Clive