Final answer:
The fifth term of the expression (x^2 + y^2)^13 is 715x^18y^8.
Step-by-step explanation:
The fifth term of the expression (x^2 + y^2)^13 can be found by using the binomial theorem.
The general term in the expansion (x^2 + y^2)^13 can be expressed as C(13,k)(x^2)^(13-k)(y^2)^k, where C(13,k) is the binomial coefficient.
In this case, we need to find the term when k is 4. Plugging in the values, we get C(13,4)(x^2)^(13-4)(y^2)^4.
Using the formula for the binomial coefficient C(n,k) = n! / (k!(n-k)!), we can calculate C(13,4) = 715.
Simplifying the expression, we get 715(x^2)^9(y^2)^4.
Finally, we can expand further to get the fifth term as 715x^18y^8.