Animal-Alphabetical Sequence
Charcoal, 83 bytes
≔AηＦ↨Ｎ⁵≔§⁺η§⪪”$⌊∧Ｘ;F‖ρ=ＪD θ⊘⊙～'ΣV⦄Ｋ◨｜]≕‖◨⟧TJρ¿¿C´!⁸⁶S/Ｕ¶V×Ｗ⧴a“,=6；‴*Þ↓h!�{≦”⁴⌕αηιηη

Try it online! Link is to verbose version of code. Explanation:
≔Aη

Start with A at the 0th index.
Ｆ↨Ｎ⁵

Input n, convert it to base 5 and loop over the digits.
≔§⁺η§⪪”...”⁴⌕αηιη

Get the current animal from the compressed string of all animal suffixes (excluding EBRA) and lookup the appropriate letter from the current digit.
η

Output the final letter.