To determine the number of real solutions for the quadratic equation \(-x^2 + 2x - 5 = 0\), we can first rewrite it in standard form, which is \(ax^2 + bx + c = 0\). In this case:
- \(a = -1\)
- \(b = 2\)
- \(c = -5\)
Next, we can calculate the discriminant, which is given by the formula:
\[ D = b^2 - 4ac \]
Substituting the values of \(a\), \(b\), and \(c\) into the discriminant formula:
\[ D = (2)^2 - 4(-1)(-5) \] \[ D = 4 - 20 \] \[ D = -16 \]
The discriminant \(D\) is negative (\(D < 0\)). This means that the quadratic equation has no real solutions.
Therefore, the answer is:
0 real solutions.