Example of "warm" -> "cold":
Notice that it's a real word each time. Can you get from "bees" -> "hive" in 5 letter changes or fewer?
Bees -> Beds -> Bids -> Bide -> Hide -> Hive
I find five solutions using only words in SOWPODS 2019, of which one has already been posted:
BEES, BEDS, BEDE, BIDE, HIDE, HIVE
BEES, BEDS, BIDS, BIDE, HIDE, HIVE
BEES, DEES, DEVS, DIVS, DIVE, HIVE
BEES, DEES, DIES, DIVS, DIVE, HIVE
BEES, LEES, LEVS, LEVE, LIVE, HIVE
Of these, I expect the third to be the most popular with the Stack Exchange crowd...
BEES -> BERS -> HERS -> HERE -> HIRE -> HIVE.
bens (high mountains)
bins (trash cans)
bine (plant stem, esp. hops - yum!)
hine (male Asian elephants without tusks; or an obsolete term for a servant)
I only had to check number 5 for validity, I'm pleased to say.
One archaic word :
Bees -> Bets -> Bits -> Bite -> Bive -> Hive
5 changes, a little archaic...
Not sure if this has already been posted so trying to take an odd route:
3. hies (old English)
4. HIVs (human immunodeficiency viruses)