Let's solve the expression step by step:

Given expression: $0.05(1.05)^{10} - 1 + 0.05$

Step 1: Calculate $(1.05)^{10}$

$(1.05)^{10} = 1.62889463$

Step 2: Multiply by 0.05

$0.05 \times 1.62889463 = 0.0814447315$

Step 3: Apply the rest of the expression

$0.0814447315 - 1 + 0.05 = 0.0814447315 - 0.95$

$0.0814447315 - 0.95 = -0.8685552685$

So, the final value of the expression is approximately:

$-0.8686$

Would you like further details or clarifications?

Here are 5 related questions:

1. What happens if you increase the exponent in the expression $(1.05)^{n}$?
2. How does changing the base from 1.05 to a larger value affect the final result?
3. What is the effect of removing the subtraction of 1 in the expression?
4. How would the expression change if the 0.05 were inside the exponent instead?
5. How can compound interest be calculated using similar expressions?

Tip: When handling exponents in compound growth formulas, small base changes can lead to large final value differences over time.