Solve: 5+5-5²+4² Using Order of Operations

$5+5-5^2+4^2=$

Let's solve the expression $5+5-5^2+4^2$ using the order of operations, also known as BODMAS/BIDMAS (Brackets, Orders (i.e., powers and roots, etc.), Division and Multiplication, Addition and Subtraction).

Here is the step-by-step breakdown:

1. Identify and calculate powers and roots first:
- Calculate $5^2$:
$5^2 = 25$
- Calculate $4^2$:
$4^2 = 16$

2. Rewrite the expression using these calculations:
$5+5-25+16$

3. Perform addition and subtraction from left to right:
- First addition: $5 + 5 = 10$
- Subtract the next number: $10 - 25 = -15$
- Finally add: $-15 + 16 = 1$

The final result of the expression $5+5-5^2+4^2$ is therefore $1$.