1 ). I (<u>want</u>) you to come to the party
Answer 1: Yo <u>quiero</u> que tú vengas al cine. <u>Quiero → modo indicativo</u>.
2). I know that you (<u>are</u>) right
Answer 2: Yo sé que tú <u>tienes</u> razón. <u>Tienes → modo indicativo.</u>
3). They asked me to (<u>believe</u>) them
Answer 3: Ellos me pidieron que les <u>creyera</u>. <u>Creyera → modo subjuntivo.</u>
4). They can't let me (<u>drive</u>)
Answer 4: Ellos no pueden dejarme que <u>conduzca</u>. <u>Conduzca → modo subjuntivo.</u>
5). He prefers me to (<u>leave</u>) my hair long
Answer 5: Él prefiere que me <u>deje</u> largo mi pelo. Deje → modo subjuntivo.
Explanation: The indicative mode expresses reality. (Yo quiero, tú tienes), but the subjunctive mode expresses doubt, possibility and hypothesis. Maybe I believed or maybe not, maybe I drive or maybe not, maybe I'll leave my hair long or maybe not.