Answer:
Just like in English we must change verbs in order to fit the structure of the sentence, so too must we do this in Spanish. Usually, depending on the structures around the verb, we will change the verb "ser" in Spanish to fit the structure and correctly deliver the message that we want. As such, the answers here would be as follows:
1. El perro (ser) es pequeño. The dog IS small.
2. Tú (ser) eres pelirrojo. You ARE a readhead.
3. Ana y yo (ser) somos delgados. We are talking about two people she and I and therefore we use somos as a variation for ser. Since Ana and I are two people, then delgado must be a plural.
4. Emilio y Luis (ser) son trabajadores. Again we have two people here, so trabajador must end with es for plural. Also, son is a variation for ser because this word is describing each of the subjects as workers.
5. Yo (m) soy paciente. In this case, ser is describing you, therefore, the variation will be soy.