The statements you listed are normal at this age. They are still learning about ownership. They also are still unsocialized beings. They just blurt out whatever they're thinking or feeling.
There is also most likely competition between the 2 girls. This is normal too.
Punishment does not change the behavior. They don't know how to be polite and make polite statements. They also don't connect their jealous statements to the time out, removing things, etc. When you think about it what does the time out tell her. It tells her she has done something wrong but a time out, etc. doesn't teach her how to relate differently. She is expressing how she feels. It will be a several more years before she'll be able to consistently control the way she expresses her thoughts and feelings.
That doesn't mean you should ignore what she says but I think you'll find that she'll behave better if you teach instead of discipline; especially when the discipline is unrated to the behavor. I would say something like "both of your pictures are good" and then perhaps talk about the pictures. If your daughter is still boastful you can acknowledge how she feels by saying "I hear that you think your picture is better. But (the other girl) also thinks her picture is better so we'll call both pictures the best." Then perhaps tape up both pictures. Or tell your daughter that you'll put her picture on the fridge when you get home.
When you do this you are modeling for her what you want her to learn. You are also acknowledging her feelings. When you treat this as a learning opportunity you reduce the anger. You describe her statements as angry ones. Perhaps she is angry because she knows she's not supposed to brag but she doesn't know a polite way to talk about her picture. The time outs etc. reinforce the anger. She feels that you don't understand how she feels.
When she says my picture is better than yours she's making a statement that communicates what she believes about her picture. She may also be expressing criticism (anger). She is in competition with the other 5 year old.
Doesn't the other 5 year old say similar things? How does her mother handle it? Often we mothers want our children to be seen as polite because on some level we believe that if they're not being "nice" it reflects negatively on our parenting. The truth is that they do not know how to express themselves in a polite way. Their brain has not matured enough for the nuances of language. Language is quite complex. At 5 kids are still at the beginning of knowing language and how to communicate. So we teach them and they gradually learn how to be polite.
If the two girls are not getting along and this is your daughter's way of expressing her unhappiness then it's appropriate to separate them. It sounds like they spend quite a bit of time together and much of this time is at the other girl's house. Your daughter may be feeling that she has to assert herself so that she feels "equal" to the other girl.
When she says "you're not saying that word correctly" she is probably saying what adults say to her.
If the other girl isn't upset about what your daughter says I recommend letting them work it out. The other girl probably says "my picture is better." If no one pays attention they may move on to another activity or subject. They "understand" each other because they both communicate in a similar manner. They will have verbal disagreements because they are learning how to get along with others. Then they receive natural consequences. One of them may say, "you're not my friend anymore!" And the other one may say it back or may have her feelings hurt. Then is the time to separate them. If your daughter is angry, say to her "sounds like you're angry so lets have a cooling off time."
Kids will say mean things to each other, hurt each other's feelings, say they're not friends or you can't play with my toy. This is all a part of learning how to get along with each other. It's normal. It's the adult's role to validate feelings and be sympathetic. Some of the time the adult can model a more polite way of saying something or a more direct approach to expressing one's feelings. For example, when intervening you could say, "sure looks to me that you're angry. Must be time to do something else." Kids can be distracted so that the negative play gets turned into something more positive. If they can't be distracted then it's a natural consequence to be separated.
If the boasting and/or angry words are not causing difficulty between the 2 girls it's best to ignore it. We reinforce behavior by giving it attention. When you discipline/punish her she may feel that this is a big deal that she doesn't understand. So she'll keep repeating it as she tries to figure out what is going on. She may realize at some point that she's not to talk that way but she has no other way to express her feelings. Her feelings are normal. She just needs to learn how to express them differently. It takes many years for kids to be able to consistently do that. Some adults never learn.
As to having no friends she will have friends. Most of the kids her age say the same things. I volunteer for playground duty and I see kids fighting, even saying "I hate you and then 5 minutes later they're back to playing together."