The first language was so faint that I kept thinking it must be some Native American language that has only old and dying speakers left, but then I realized that the languages are (I’m pretty sure of this):

1. Afrikaans
2. Bulgarian
3. Hakka
4. Greek
5. Malay

Without checking and comparing the recordings on the Omniglot useful phrases ‘Happy New Year’ page. I can only comment on the two languages I initially recognise.
2 is something Slavic because I recognise part of the phrase ‘nova godina’ but I know it’s not Polish because that would be traditionally ‘Nowego Roku’ in Polish. So I’m guessing either Serbian or Bulgarian (Нова Година)?
4 is definitely Greek Καλή Χρονία ‘kali chronia’

Καλή Χρονία σε όλους! (Happy New Year everyone!)

Guesses

1. Hebrew?
2. Slavic, maybe Bulgarian
3. Something Sinitic
4. Greek (sure)
5. Malay (or Malayo-something)

@yenlit in Polish it’s either Szczęśliwego nowego roku! or Do siego roku! the second seems to be going out of usage though : (

@Michael Farris

Masz rację, dzięki! I was a bit clumsy the way I wrote it and what I meant to include was ellipsis ‘…. Nowego Roku’ because I was comparing the Polish to the corresponding ‘…. nova godina’ portion of the Serbian/Bulgarian recording. Of course ‘New Year’ in isolation is ‘Nowy Rok’.

Szczęśliwego nowego roku!

1. Dutch 2. Bulgarian 3. Thai 4. Greek 5. Persian

(These thoughts are from before reading the comments above — honest! — though I’m pleased they seem to accord with my guesses:)

2. Slavic (though I can’t name the precise language), because of the recognizable “novo godino”, or something like it, for “new year”
4. Greek, because of the recognizable “hroniá”, which must surely have something to do with (the) TIME (of year)!

The answers are:

1. Afrikaans = Gelukkige nuwe jaar
2. Bulgarian (български) = Честита нова година (Čestita nova godina)
3. Hakka (客家話) = 新年快樂 (sin1-ngien2 kuai5-lok8)
4. Greek (Ελληνικά) = Καλή χρονιά! (Kalí hroñá)
5. Malay (Bahasa melayu) = Selamat Tahun Baru