I'm not sure what the problem was. It works for me in 10.3.
In[1]:= $Version
Out[1]= "10.3.0 for Microsoft Windows (64-bit) (October 9, 2015)"
In[2]:= f[x_] := {{x*5, x^2}, {x, x - 1}}
In[3]:= f[x]
Out[3]= {{5 x, x^2}, {x, -1 + x}}
In[4]:= f[x][[2, 2]]
Out[4]= -1 + x
In[5]:= f[3]
Out[5]= {{15, 9}, {3, 2}}
In[6]:= f[3][[2, 2]]
Out[6]= 2
