Take the first letter of each object in the cabinet and put them together to spell out the 5-digits of the code. Each row of alcoves gives you one digit in the code: the top row is the first digit, the second row is the second digit and so on.
Row 1 – Tooth, Head, Ring, Egg, Eagle = T H R E E
Row 2 – Scorpion, Eye, Vase, Elephant, Nest = S E V E N Row 3 – Fish, Insects, Vase, Egg = F I V E
Row 4 – Owl, Necklace, Eel = O N E
Row 5 – Earwig, Iron, Globe, Horseshoe, Trilobite = E I G H T