You can refer to the blog - Death Note, Vol. 4: Love (Death Note #4) about the summary of the previous volume.
After Light gives up his Death Note and all memories of it, he is convinced that he's innocent despite he has been locked up for a week. However, L still suspects Light especially the killings stopped once Light was incarcerated.
Then a different pattern of Kira crimes hits Japan. Someone else has the Death Note and these new deaths are more focused on making money. The killings are targeting on a corporate's rival company and the corporate definitely is the biggest suspect but who is Kira or who is having the Death Note now?
The story is getting more complicated and confusing for me. I started can't think in a proper way especially there are too many rules for using the Death Note. However, no matter how complicated this story going to be, I never feel regret to pick this story as my first manga reading. I'm not sure both L and Death Note can be replaced any other characters and manga that I'm going to read in the future.
More reviews can be found on Goodreads: Death Note, Vol. 5: Whiteout (Death Note #5).