Solve: Finding the Sum of 25,306 + 10,070

To solve this addition problem, we will perform the following steps:

• Step 1: Align the numbers $25,306$ and $10,070$ by their place values for proper addition.
• Step 2: Begin adding from the rightmost digit (units), moving towards the left.
• Step 3: Handle carrying over when sums of digits exceed 9.

Let's work through this:

Step 1: We write the numbers vertically aligning their digits by place value:

$\begin{array}{c} & 2 & 5 & 3 & 0 & 6 \\ + & 1 & 0 & 0 & 7 & 0 \\ \hline \end{array}$

Step 2: Start adding from the units column:

Units Column: $6 + 0 = 6$

Tens Column: $0 + 7 = 7$

Hundreds Column: $3 + 0 = 3$

Thousands Column: $5 + 0 = 5$

Ten-Thousands Column: $2 + 1 = 3$

Thus, the final result of the addition is $25,376$.

Therefore, the sum of $25,306$ and $10,070$ is $\mathbf{25,376}$. This matches the provided choice labeled as:

Choice 2: $\boxed{25,376}$

Thus the solution concludes with result:

The correct answer is:

$\boxed{25,376}$