Suppose you have 5 pith balls of unknown charges. You are told that A experiences a force of attraction near a glass rod rubbed with plastic, B...

Hello!

As I understand, the question is what charges these balls have. Each can be positively charged (+), negatively charged (-) or neutral (0).

It is well known that the same charges are repelled and the opposite are attracted. Also it is a well known phenomenon that neutral dielectric bodies are attracted to charged bodies, both positively and negatively. Note that neutral body is never repelled.

Also we need a starting point: what is the charge of a glass rod rubbed with plastic? The triboelectric series helps here, see the link. From it we know that glass becomes positively charged when rubbed by plastic.

1. C repels the glass rod (+) means C is also (+).

2. B repels A means they have the same charge and are not neutral.
A is attracted to the glass rod so A is (-) and B is (-).

3. D repels B so D is (-).

4. E is attracted to C (+) and D (-), so E cannot be (+) or (-), it is (0).

The answer: A is negative, B is negative, C is positive, D is negative and E is neutral.