Lena isn't mad just because Kara kept her double-life secret.

Haven't seen 5x08 yet, so this is my reading of the based on previous episodes.

Kara keeping up the illusion that she and Supergirl and separate beings is part of why Lena's mad, but not the full picture. What Lena *wrongly* thinks, largely in part to having the secret revealed to her by Lex and his twisted version of events and the James Espionage incident in S3, is that Lena currently thinks her entire friendship with Kara, and by extension everyone else on the SuperFriends team is a lie. that they all played a part in so that they could spy on Lena and [pre-emptively stop any evil schemes she *might* come up with.](https://youtu.be/dNPkJ7eEVDU?t=49) This would mean that none of them ever trusted her, they all actually believed Luthors were untrustworthy at best, genetically bad at worst. In the meantime, until such a situation should arise, they would take advantage of having a billionaire genius "friend" to handle other situations.

In short, Lena thinks the friendship was at best, only transactional in nature. Her intellect and resources and in return they act as her friends. Similar to what Eve, Andrea, Rhea actually did (granted Andrea and Eve acted under duress). We also can't forget that Lena has been putting all her grief in little boxes that have all sprung open at the same time and they have come back to haunt her since the end of S4E22 and there's a months gap between that and the start of S5E1.

But we the audience have known that for a long time that isn't the case. Kara has almost entirely trusted and respected Lena since their first meeting. Kara also brings everyone in her circle around when they have various degrees of doubt about Lena's true motives, because Kara believed in her. It was fully understandable back in S2E1 that Kara "investigated" Lena as they hadn't met before. It becomes an issue in S3 when Lena wants to help Sam and isn't sure what the DEO would do to Sam when they learned Sam was Reign and the synthetic Kryptonite debacle and Kara then continues pretending she's not Supergirl, so that she can still be Lena's friend after making a mistake.