To find the dimensions of the planted area of the square garden, we can proceed step-by-step:

Step 1: Define variables

Let $x$ be the side length of the planted square garden (without the walkway). The walkway is 5 feet wide all around, so the total side length of the garden including the walkway will be $x + 2(5) = x + 10$ feet.

Step 2: Total area (including walkway)

The total area of the garden, including the walkway, is given as 10,000 square feet. So, the equation for the total area is: $(x + 10)^2 = 10,000$

Step 3: Solve for $x$

Now solve for $x$: $x + 10 = \sqrt{10,000} = 100$ $x = 100 - 10 = 90$

Step 4: Conclusion

The side length of the planted area is 90 feet. Since it's a square garden, the dimensions of the planted area are: $\boxed{90 \text{ feet} \times 90 \text{ feet}}$

Would you like more details or have any further questions?

Here are some related questions to explore:

1. What is the perimeter of the planted area?
2. How much area is covered by the walkway alone?
3. What would the dimensions be if the walkway was 10 feet wide instead?
4. How would the dimensions change if the total area was reduced to 8,000 square feet?
5. How would you solve this problem if the garden was a rectangle instead of a square?

Tip: When solving geometry problems with additional structures like walkways, always start by defining the variables for the core area and then account for the added dimensions systematically.