Is it possible to compute the eigenvalues and eigenvectors if I know the svd?

Question

I have a matrix $A$

A =

2.00000    3.00000    1.00000    0.50000    4.00000
4.00000    5.00000    7.00000    0.10000    1.00000
5.00000    3.00000    6.00000   19.20000    9.00000
1.00000    4.00000    1.00000    4.00000    7.00000
3.00000    1.00000    6.00000    2.00000    6.00000

I did the SVD on matrix $A$.

[U,S,V] = svd(A)

U =

-0.149403  -0.278046  -0.422317  -0.209000   0.823612
-0.198548  -0.731899   0.473681  -0.422812  -0.147509
-0.872587   0.409042   0.244648  -0.055987   0.091043
-0.304238  -0.128976  -0.728923  -0.262419  -0.539085
-0.290325  -0.450625  -0.078065   0.839971  -0.031671

S =

Diagonal Matrix

25.63602          0          0          0          0
       0   10.08558          0          0          0
       0          0    6.01867          0          0
       0          0          0    3.71319          0
       0          0          0          0    0.98157

V =

-0.2586652  -0.2894557   0.2176915  -0.0354640   0.8947963
-0.2171159  -0.4197117  -0.1924603  -0.8399028  -0.1850004
-0.3440842  -0.5730769   0.5257015   0.3427795  -0.3991605
-0.7273295   0.6171432   0.2428507  -0.1592856  -0.0760113
-0.4884167  -0.1754271  -0.7617289   0.3878607   0.0027517

But then when I checked the eigenvalues and eigenvectors, they where not the same.

[v, e] = eig(A)
v =

  -0.18903 + 0.00000i   0.15906 - 0.21827i   0.15906 + 0.21827i  -0.87710 + 0.00000i  -0.20055 + 0.00000i
  -0.39291 + 0.00000i   0.25894 + 0.33885i   0.25894 - 0.33885i   0.15307 + 0.00000i  -0.83881 + 0.00000i
  -0.74945 + 0.00000i  -0.69885 + 0.00000i  -0.69885 - 0.00000i   0.42831 + 0.00000i   0.12425 + 0.00000i
  -0.30382 + 0.00000i   0.12855 - 0.36818i   0.12855 + 0.36818i   0.13432 + 0.00000i  -0.05592 + 0.00000i
  -0.39484 + 0.00000i   0.17079 + 0.27486i   0.17079 - 0.27486i  -0.07597 + 0.00000i   0.48746 + 0.00000i

e =

Diagonal Matrix

   21.3589 +  0.0000i                    0                    0                    0                    0
                    0   -1.9810 +  6.6826i                    0                    0                    0
                    0                    0   -1.9810 -  6.6826i                    0                    0
                    0                    0                    0    1.2580 +  0.0000i                    0
                    0                    0                    0                    0    4.3450 +  0.0000i

As you can see, the matrix $A$ have complex eigenvalues, but not in the $S$ matrix of SVD. Why? Is it possible for me to compute the eigenvalues and eigenvectors from svd if I know $A,U,S,V$?