There are plenty of similarities between The Last Jedi and The Empire Strikes Back. Both Star Wars movies continue the stories of heroes struggling to defeat a tyrannical galactic government that rules with an iron fist. In The Last Jedi, it's up to Rey, Finn, Poe, Luke, and Leia to stop Supreme Leader Snoke and the First Order once and for all.
While The Last Jedi left us with plenty of unanswered questions, writer-director Rian Johnson clearly used Episode V as the model for his depiction of the Resistance. In the same way that The Force Awakens emulates A New Hope, at times, The Last Jedi perfectly emulates The Empire Strikes Back.
Below are the best examples proving that. Be warned, though. There are spoilers ahead.
Although both A New Hope and The Force Awakens end in Rebel victories, their sequels present the Rebel force in dire situations. The Empire and the First Order are both upset that their respective super weapons are shattered by the do-gooders. Accordingly, the bad guys are out for revenge. Both The Empire Strikes Back and The Last Jedi begin with the Rebels escaping from a base as the enemy shows up.
The Empire Strikes Back took the characters from A New Hope and split them into smaller groups in order to further explore each hero and flesh out their respective stories. The Last Jedi takes a similar approach, splitting the heroes in three: Rey's on Ahch-To with Luke, Finn goes on an adventure with Rose to Canto Bight, and Poe and Leia are leading what's left of the Resistance. After all of the trials and tribulations, the heroes in both The Empire Strikes Back and The Last Jedi are (mostly) reunited in the final moments of the third act.
Besides the fact that both planets have white surfaces - Hoth is covered in snow and Crait in salt - two very similar battles take place in each location. The Empire and the First Order both bring massive walkers to take down the Rebel and Resistance bases, and ultimately succeed, although the remaining good guys manage to escape them in order to fight another day.
Viewers didn't know the truth about Luke's father was coming in The Empire Strikes Back, making Darth Vader's revelation one of the most shocking moments in cinema history. In The Last Jedi, Star Wars fans know to expect a big reveal about Rey's parents but it's still shocking to learn the truth about them. In fact, Rey's parental revelation is one of the major plot points in the film. Both Luke and Rey learn the truth about their parents while facing major villains.