I'm re-watching Dark Matter (before I see Season 2) so this answer will be added to as I go along.
As Bruno said, in episode 4, Two killed several Casino employees in front of Five. Five was naturally very shocked (she flinched away from Two, stammering "Y-y-y-you-you kill..." before Two grabbed her by the arm and dragged her out of the casino basement).
At the end of the episode, Two wanted to talk to Five about the incident but Five didn't want to talk about it and left the room when Two insisted they discuss it.
This would be the point at which Five stopped trusting Two. Further incidents are given below, to show how the trust between Five and Two fluctuates.
In episode 5, Five asks the Android to keep the card she found a secret.
Five: Do me a favor, don't tell any of the others about this, okay?
Android: I thought you had resolved to trust them. Well, some of them anyway.
Five: Yeah, so did I.
However later in the episode Five states that she doesn't want Two (and One and Three) to die, so although she may not trust Two completely, she doesn't consider Two to be such an untrustworthy person that she deserves to die.
When Two brings up the casino incident later on in this episode, she states that she didn't mean to kill the men.
Two: Look, about what happened on the space station I'm sorry you had to see that. I didn't mean to kill those men. It was just...
Two: I was going to say reflex. I wasn't ready, I wasn't in control. Next time it'll be different.
So Two is trying to tell Five that she is trustworthy, and I think that at this point Five may trust Two a bit more than she did immediately after the casino incident but not enough to reveal any major secrets.
In episode 6, before Five dives into the memories, Two is very concerned and tries to stop her. Eventually, Two gives in but still provides reassurance to Five.
We'll be monitoring your vital signs. If anything goes wrong, we'll pull you out
Two holds Five's hand tightly
Later on, when Five gets pulled out, she asks why and Two responds (vehemently):
Because I don't want you to have a stroke, that's why. Hey, this was a bad idea. **
Later on, Two and One volunteer to help Five but Six overrules them and goes to rescue her. At the end of the episode, they have this conversation:
Five: You know, it's one of the reasons why I didn't want to come back. I never felt like I knew who to trust out here. I mean, I thought I could trust Two, but sometimes she scares me a little.
Six: Yeah, join the club.
Five: But now, at least, I know I can trust you.
So it looks as though at this point, Five trusts Two a bit more than she did in episode 5, but still isn't sure about it.
More to come...
**In his response to this question @Bruno says that "Both occasions revealed the "true" nature of Two's character: a dangerous murderer." However her actions here show that Two is not (at the core) a bad person.