(2024^5 + 1)/(2024^4 - 2024^3 + 2024^2 - 2023)

To simplify the expression

\[
\frac{2024^5 + 1}{2024^4 - 2024^3 + 2024^2 - 2023},
\]

let's first analyze both the numerator and the denominator.

### Step 1: Simplify the numerator
The numerator \( 2024^5 + 1 \) can be factored using the sum of cubes identity:

\[
a^3 + b^3 = (a + b)(a^2 - ab + b^2).
\]

However, in this case, we can rewrite \( 2024^5 + 1 \) in a form useful for factoring:

\[
2024^5 + 1 = (2024 + 1)(2024^4 - 2024^3 + 2024^2 - 2024 + 1).
\]

### Step 2: Simplify the denominator
Let’s analyze the denominator:

\[
2024^4 - 2024^3 + 2024^2 - 2023.
\]

Instead of factoring this directly, let's substitute \( x = 2024 \) for clarity:

The expression becomes

\[
\frac{x^5 + 1}{x^4 - x^3 + x^2 - 2023}.
\]

The denominator \( x^4 - x^3 + x^2 - 2023 \) can also be factorized or fed into the division, but it’s useful to see if it can be derived from the numerator’s structure.

### Step 3: Check for common factors
Notice that the numerator has factored as:

\[
(x + 1)(x^4 - x^3 + x^2 - x + 1).
\]

This indicates there might be a similar structure in the denominator. Thus, we can evaluate:

When substituting \( x = 2024 \), we see if \( x^4 - x^3 + x^2 - 2023 \) can yield tangible outcomes.

### Step 4: Final Evaluation
Now, since both the numerator and denominator share the term \( x^4 - x^3 + x^2 - x + 1 \), we can reduce the overall expression:

\[
\frac{(2024 + 1)(2024^4 - 2024^3 + 2024^2 - 2024 + 1)}{2024^4 - 2024^3 + 2024^2 - 2023} = 2025 \cdot \frac{2024^4 - 2024^3 + 2024^2 - 2024 + 1}{2024^4 - 2024^3 + 2024^2 - 2023}.
\]

Evaluating \( \frac{2024^4 - 2024^3 + 2024^2 - 2024 + 1}{2024^4 - 2024^3 + 2024^2 - 2023} \) results in a single unit when simplified further.

Thus, the final answer is:

\[
2025.
\]