Sometimes this error can happen if you are exhausting your PHP memory limit. Use our tutorial on how to increase PHP memory limit in WordPress to fix that.
If you are seeing the internal server error only when you try to login to your WordPress admin or uploading an image in your wp-admin, then you should increase the memory limit by following these steps found on Wordpress.org
If increasing the memory limit fix the problem for you, then you have fixed the problem temporarily. The reason why we say this is because there has to be something that is exhausting your memory limit. This could be a poorly coded plugin or even a theme function. We strongly recommend that you ask your WordPress web hosting company to look into the server logs to help you find the exact diagnostics.
If increasing the PHP memory limit did not fix the issue for you, then you are in for some hard-core trouble shooting.