¿Cuál es la diferencia entre "últimamente" y "recientemente" ?Puedes dar oraciones como ejemplo.

Últimamente is something you’ve been doing for days or constantly from one moment to the next you started to do it (like lately)

Example:
“Últimamente me he sentido muy cansada después del trabajo, creo que es porque no he dormido bien”

“Lately I've been feeling very tired after work, I think it's because I haven't slept well”

And recientemente most of the times mean something that you didn’t so long ago (recently)

Example:
“Jorge empezó a estudiar gastronomía recientemente” (da a entender que es reciente, hace poco tiempo)

“Jorge recently started studying gastronomy" (implying that it’s recent, a short time ago)

But I think is not a big difference just like Recently and Lately