Answer:
1. Nos gustan los perros porque son amigables
In this kind of examples, the verb "gustar" (to like), must match the object "los perros" (the dogs) in number, the plural form adds an "n" at the end. Therefore the only correct answer is "nos gustan", since the other options are singular.
2. Me gusta mucho visitar museos de arte contemporáneo
The difference with number 1 is than in this one the object is not "los museos" (the museums), but the act of visiting museums, which makes the verb require a singular form since it's only one action that is liked, therefore the correct answer is "me gusta". If we eliminated the verb "visitar" (to visit), "me gustan" would be the right answer.
3. A los jugadores les gustaría ganar todos los partidos
Unlike the previous example, this sentence is supposing that players would like to win not making a statement, meaning it's a subjunctive sentence rather than indicative. However, the noun is third person plural, which means the pronoun must also be third person plural.
4. Me gustaria ir a la ópera algún día.
The object is a singular, which means the verb cannot be plural, so the only correct answer is "me gustaría" (I would like)
5. No nos gustaría llegar tarde al concierto
Same as in sentence number two, the object is a single action "llegar tarde al concierto" (arrive late to the concert). Therefore we use a singular form, so the only option is "nos gustaría"