Meta: Root's message for Shaw
In 4x05, Root says, "if the worst comes to pass, if you could give Shaw a message?" when she believes she will die in the fight against Martine. Although we don't hear the exact wording of this message, the context and Finch's reply of "I think she already knows", tell us it is a declaration of love.
Then in 5x13 when the Machine is fading, She tells Shaw, "There's something I think Root had wanted to say to you. You always thought there was something wrong with you because you don't feel things the way other people do. But she always felt that was what made you beautiful. She wanted you to know that if you were a shape, you were a straight line. An arrow."
During their time together, Root's flirting consists of exaggerated innuendo to push Shaw's buttons ("I'll do yours if you do mine" in 3x23, "I love it when you play doctor" in 3x17), and in return Shaw pushes Root's buttons by aggressively pretending she doesn't care about Root ("I missed you like I'd miss an intestinal parasite" in 3x20, "I wouldn't want anything to happen…to the dog" in 4x10). Root never disrupts the delicate balance of this dance, never asks Shaw for more than she's willing to give or demands any confirmation of her feelings, beyond light teasing such as "and is that why you came to see me?" in 4x07.
But in the event of her death, she wants Shaw to know the true extent of her feelings. Given that she always intended it to be this way, this means the message isn't for her benefit - it's for Shaw's. She wants Shaw to know beyond a shadow of doubt that Root loved and understood her for exactly who she is, and has no expectations for what her grieving process should look like. She doesn't want Shaw to ever feel like she isn't enough.
A variation of this also appears in 4x11. In one of the Machine's simulations, Root calls Shaw while knowing she doesn't have long left and it is the only time we see her push for any sort of confirmation about their relationship. She says, "Why are you so afraid to talk about your feelings? [...] We're perfect for each other. You're gonna figure that out someday." and is elated with Shaw's reply that "maybe someday [...] we can talk about it."
Since the Machine is able to accurately predict Her assets and knows Root's final request well enough to carry it out in 5x13, She knows this is the one situation where Root would push the issue enough to make it clear that she loves Shaw and that she would be thrilled with any degree of confirmation Shaw chooses to give.
Their conversation in the real timeline begins in exactly the same way, with Root in a dire situation calling Shaw to say, "Hey, sweetie. You busy?". Shaw replies, "A little. Skip the verbal foreplay, Root. Why are you calling?" and Root says, "Can't a couple of gals take a little break from work to catch up?". However, at this point Shaw arrives in the stock exchange and the team's chance of survival increases considerably.
The rest of their conversation plays out similarly, but is toned down. Root says, "We're so good at this together. You're gonna realize that someday." Where the simulation began with Root asking a direct question about Shaw's feelings, this is an open statement that doesn't put any pressure on Shaw to respond.
Shaw replies, "Root, no offense. You're hot, you're good with a gun. Those are two qualities I greatly admire. But you and me together would be like a four-alarm fire in an oil refinery." Just like how Root in the simulation was happy with Shaw's response, she cheerily replies, "Sounds cozy." Since at this moment her life is no longer in immediate danger, she doesn't feel the need to say anything further.
