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The number is 345.
Explanation
Since the number is odd and is divisible by 5, its last digit (the ones digit) is 5.
Its tens-digit is less than 5, and its first digit (the hundreds digit) is 2 or 3.
So, the number is EITHER 345 OR 235 OR 245.
But the two last candidate numbers are not divisible by 3 (the sum of their digits is not a multiple of 3).
So, the only possibility is the number 345, which satisfies all conditions.
Solved.