If ax^2+bx+c=0
is a quadratic equation then D=b^2-4ac is the discriminant.
Now if D<0 then this equation would have complex roots.
Our equation is x^2+2x+5=0
Then D=2^2-4*1*5=-16<0
Hence this equation would not have any real root.
Now if you want to find the complex root you can find it using Sridhar acharya
The roots are
-1+2i and -1-2i