So say the novel is written in first-person tense. a chapter ends, and the next chapter starts 10 days later. Here I start narrating something that happened 5 days ago in past tense as a flashback.
So instead of day1(present) > day5(present) > day10(present)
I go day1(present) > day10(present) > day5(past. Flashback/backstory)
Do you think this would add variety to the writing? Or just be too distracting of an excuse to break from the present-tense writing?
I recommend you reading "Six Walks in the Fictional Woods" by Umberto Eco. He explains in the book such narratives (and many other aspects of either ommiting parts of information or stating it in achronological order).
The short answer to you question is: yes, you obviously can do that. Just remember (as Monica Cellio commented) to clearly state that the situation is back in time. It does not mean you need to give time clearly, but the reader should know somehow what is the correct order of events (unless you intentionally want him to be uncertain, which could be a point if it is criminal story and the protagonist is a detective reconstructing events). On the other hand you should not give more clues than necessary.
Fine way to introduce such flashback is to use parts of the story world rather than exact time. You could even introduce some object/person into your story just to mark the time. E.g. in first chapter a cat walks around your flat and (at the end) destroys your favourite cup; in second one cat is already dead (and obviously cup is gone); then in third you do not give clues about time, but cat is alive and the cup is broken. This way both the reader knows at which time events occure and the story does not become boring.
It's fine to use flashbacks, but you should make sure you're doing it for a reason, rather than "just to mix things up."
For instance, you could give us
day 1 (present, Character 1) -> day 10 (present, Character 1) -> day 5 (past, Character 2)
if you want to reveal Character 2's actions after you reveal how Character 1 reacted to the results of those actions (i.e. to build suspense), or if C1 and C2 aren't interacting and it's more streamlined to split their actions up. But don't just scramble your timeline to no purpose.
Agree with MissMonicaE's answer. If you feel you need to change the sequence of events "just to mix things up", then your story was boring. Now it is boring and confusing. All other things being equal, people prefer linear storytelling.
For example, Tolkien skillfully uses nonlinear storytelling in Lord of the Rings, but only because he must -- he often has 3 (or 4!) separate groups doing stuff at the same time. Rather than referring to dates (that the reader won't remember), he refers to events that all his groups experience. Occasionally the narrator reminds the reader what the other groups are doing. Or, characters from one group will fill in other characters on what their group was doing. (So the reader gets both narrative, self-commentary, and interaction, all in one passage.)
Of course, other writers do this. Victor Hugo, Charles Dickens, Shakespeare. It's a classic technique. Even Homer does it.
Summary: Flashbacks are great, but only use them when they serve a distinct purpose, because they DO make it harder on your reader.
