#### Answer

Discriminant: $-60$;
Roots/solutions: Two imaginary numbers which will be complex conjugates of one another.

#### Work Step by Step

Let us determine the discriminant of the quadratic equation $5x^2+3=0$
which can be calculated as: $D=b^2-4ac=(0)^2-(4)(5)(3)=-60$
This implies that $D$ represents a negative real number and with solution of two imaginary numbers.
Hence, our answer is:
Discriminant: $-60$;
Roots/solutions: Two imaginary numbers which will be complex conjugates of one another.