1. **State the problem:** We need to find how many odd numbers between 1 and 2025 are not divisible by 5. 2. **Identify the total odd numbers from 1 to 2025:** Odd numbers are every other number starting from 1. The formula for the count of odd numbers up to an odd number $n$ is $\frac{n+1}{2}$. Calculate total odd numbers: $$\frac{2025 + 1}{2} = \frac{2026}{2} = 1013$$ 3. **Count odd numbers divisible by 5:** Odd numbers divisible by 5 are multiples of 5 that are odd. Since 5 is odd, multiples of 5 alternate odd and even: 5 (odd), 10 (even), 15 (odd), 20 (even), etc. To find how many odd multiples of 5 are there up to 2025, find how many multiples of 10 are there (since every second multiple of 5 is odd): Number of multiples of 5 up to 2025: $$\left\lfloor \frac{2025}{5} \right\rfloor = 405$$ Since odd multiples of 5 occur every other multiple, number of odd multiples of 5: $$\left\lceil \frac{405}{2} \right\rceil = 203$$ 4. **Calculate odd numbers not divisible by 5:** $$\text{Odd numbers not divisible by 5} = \text{Total odd numbers} - \text{Odd multiples of 5} = 1013 - 203 = 810$$ **Final answer:** There are $\boxed{810}$ odd numbers from 1 to 2025 that are not divisible by 5.