Show that no number of the form 8k + 3 or 8k + 7 can be written in the form $a^2 +5b^2$ I'm studying for a number theory exam, and have got stuck on this question. 

Show that no number of the form $8k + 3$ or $8k + 7$ can be written in the form $a^2 +5b^2$

I know that there is a theorem which tells us that $p$ is expressible as a sum of $2$ squares if $p\equiv$  $1\pmod 4$.
This is really all I have found to work with so far, and I'm not really sure how/if it relates.
Many thanks!

$8k+3,8k+7$ can be merged into $4c+3$ where $k,c$ are integers
Now, $a^2+5b^2=4c+3\implies a^2+b^2=4c+3-4b^2=4(c-b^2)+3\equiv3\pmod 4,$ 
But as $(2c)^2\equiv0\pmod 4,(2d+1)^2\equiv1\pmod 4,$
$a^2+b^2\equiv0,1,2\pmod 4\not\equiv3$
Clearly, $a^2+5b^2$ in the question can be generalized $(4m+1)x^2+(4n+1)y^2$ where $m,n$ are  any integers
