Hello! "A finales de mayo" would be the correct one. Every time you want to say "at the end of" and a month you should use "a finales de". "Término" is too formal and most of us don't use it very often. In fact, when reading "término" I first thought about the noun "term". "Fin" is a noun. You would never use it as "at the end of". You can say "al fin" but it means "Finally", for example when you're waiting for someone and he arrives late: ¡Al fin llegas!. If you want to say "at the end of the class", for instance, that would be "al final de la clase". I hope I have been helpful!

Hallo Tim, "At the end of May" = A final de mayo. "A finales de mayo" means that it is around/before the end of May. "by the end of May". The question is somehow broad, because each of the three words has different meanings and could be used in many situations. Al término/final de los 90 minutos ocurrió el final del partido y la copa del mundo llegó a su fin/final. Por fin podemos descansar del fútbol. ¿Con qué fin/finalidad aprendemos idiomas?

Mmmm... - 'Fin' o 'Final' can be used alone. It would be like "The end". If you want to use like "the end of something"; you have to use also "el" before. For example: El FIN de los tiempos / El FINAL del viaje. You can use both in that two examples. But, you have to consider that FIN can be also a noun (similar to "goal"). For example: No tenía un FIN concreto / El FIN no justifica los medios. In those cases are used like nouns. - 'Final' o 'Finales' are more used when you refer to the end of something. For example: El FINAL de la película / A FINALES de mes. And they can be used like adjectives; for example: Los exámenes FINALES / La parte FINAL. - Término really refers to the last part of something. But it has more different meanings, so it is more risky if you don't know what really means. It can be used like noun (similar to "word"), and in comparision with "fin" and "finales"; it is commonly used with "a" before "término". For example: Llevó a TÉRMINO (He finished), but in general, it isn't so frequently used.