We can simplify question to:
(n-1)(n+3-n+2) = m(n-1)
(n-1)*5 = m*(n-1)
m*(n-1) - 5*(n-1) = 0
(m-5)*(n-1) = 0 ............. (A)
Now, stmt 1: |m| = 5, i.e. m=5, or m = -5
If m = 5, then (A) becomes 0*(n-1) = 0, so n can be any value.
If m = -5, then (A) becomes -10*(n-1) = 0 or n = 1
Hence insufficient. Eliminate A,D
Now, stmt 2: m = 5, similar to above, (A) becomes 0*(n-1) = 0, so n can be any value.
Hence Insufficient. Eliminate B
Now, Combined, we get the condition, m = 5, again (A) becomes 0*(n-1) = 0, so n can be any value.
Hence insufficient. Eliminate C.
So as per my analysis, answer should be
Option E
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