The problem is 5x to the 3rd times (7x)squared.

I multiplied (7x)(7x) first and got x squared + 14x + 49. Then I multiplied each of those by 5x to the 3rd and came up with an answer of: 5x to the 5th + 70x to the 4th + 245x to the 3rd. Did I get this one correct??

<<I multiplied (7x)(7x) first and got x squared + 14x + 49.>>

Well you did that wrong, as well as some other steps.
(7x)^2 = 49x^2
The polynomial you wrote is (x+7)^2

5x^3*(7x)^2 = 5*49 x^5 = 245 x^5

To solve the problem, you need to follow the rules of exponents and distribute the terms correctly. Let's break down the problem step by step:

Step 1: Multiply (7x)(7x) to get (7x)^2= 49x^2. You have correctly completed this step.

Step 2: Multiply the result from step 1 by 5x^3. To do this, you need to multiply each term in the result by 5x^3:

(49x^2) * (5x^3) = 245x^5.

So, you correctly determined the first term as 245x^5.

Step 3: Now, let's calculate the second term. Multiply each term in the result from step 1 - 49x^2 - by 5x^3:

(14x) * (5x^3) = 70x^4.

Therefore, the second term is 70x^4.

Step 4: Finally, calculate the third term. Multiply the constant term in the result from step 1 - 49 - by 5x^3:

(49) * (5x^3) = 245x^3.

Hence, the third term is 245x^3.

So, after multiplying everything correctly, the final result should be:

245x^5 + 70x^4 + 245x^3.

Therefore, your answer is incorrect. The correct answer is:
245x^5 + 70x^4 + 245x^3.