1. **State the problem:** We are given the quadratic equation $$kx^2 + 5x = -7$$ and need to find all values of the constant $$k$$ such that the equation has two distinct real solutions. 2. **Rewrite the equation in standard form:** Move all terms to one side: $$kx^2 + 5x + 7 = 0$$ 3. **Identify coefficients:** Here, $$a = k$$, $$b = 5$$, and $$c = 7$$. 4. **Condition for two distinct real solutions:** The discriminant $$\Delta$$ must be positive: $$\Delta = b^2 - 4ac > 0$$ 5. **Substitute coefficients:** $$5^2 - 4 \cdot k \cdot 7 > 0$$ $$25 - 28k > 0$$ 6. **Solve inequality for $$k$$:** $$25 > 28k$$ $$k < \frac{25}{28}$$ 7. **Conclusion:** The quadratic equation has two distinct real solutions if and only if $$k < \frac{25}{28}$$. **Final answer:** $$\boxed{k < \frac{25}{28}}$$