1. **State the problem:** We are given two equations: $$x^2 - y^2 = 30$$ and $$x - y = 5$$ We need to find the value of $$(x + y)^2$$. 2. **Recall the identity:** Notice that $$x^2 - y^2 = (x - y)(x + y)$$. 3. **Substitute the known value:** Using the given equations, $$x^2 - y^2 = 30$$ and $$x - y = 5$$, so $$(x - y)(x + y) = 30$$ which means $$5 imes (x + y) = 30$$. 4. **Solve for $x + y$:** $$x + y = \frac{30}{5} = 6$$. 5. **Find $(x + y)^2$:** $$ (x + y)^2 = 6^2 = 36$$. **Final answer:** $$(x + y)^2 = 36$$.