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Solution

We have 5 digits → total 5! = 120 numbers. Numbers greater than 23000 must start with 3, 4, or 5. For each case: Start with 3,4,5 → remaining 4 digits can be arranged in 4! = 24 ways each. Total = $3 \times 24 = 72$. Additionally, numbers starting with 2 are not all smaller (only those starting 23,24,25). For 24 and 25 → also possible 24 numbers. Total = $72 + 18 = 90$.