Hello Suri, welcome to the forum! Dwarf rabbits are a lot more skittish by nature than larger breeds, and it may take a while anyway before she has enough courage to seek you out and to leave her cage. We have a Netherland Dwarf called Breintje and it took him weeks to get adjusted in my home. There are several bonding exercises you can do with her. Here are some good tips for getting to know eachother and to adjust to the new living area:

https://www.wikihow.pet/Bond-With-Your-Rabbit
http://language.rabbitspeak.com
https://www.wikihow.com/Calm-a-Rabbit

Now for the practical problem at hand: she’s going to have to learn to be picked up anyway. One day she’ll have to go into a carrier to go to the vet, her nails will need to be done regularly, etc. It’s true that rabbits hate being picked up and you shouldn’t do it daily, but it’ll be necessary in certain situations. So best start out now and make it as pleasant as possible.
I’d give her a small treat (raisin, small piece of fruit) first to show her that something good is happening. Make sure that you feel as calm and confident as possible during the process. I’m quite sure that rabbits feel our moods: if you’re nervous, she’ll be too. Gently pet her with you hand and put your hand flat on her neck area to establish a bit of contact. Pick her up gently while supporting her hind quarters and place her in a carrier or box where she can’t fall out of. When you’ve cleaned the cage do the reverse and gently put her back. End with a treat and stay near the cage to alk to her gently and to pet her if she allows that. Rabbits are sensitive to intonation, and using words like “good girl!” will help her to know which behaviour is desirable.

If you’re not familiar with picking up a rabbit: https://www.wikihow.com/Pick-up-a-Rabbit
Personally I’m not a fan of picking up rabbits by the scruff of their neck, even if you’re supporting their rear end. I prefer the “supported by arms on all sides method”, while gently pressing Breintje against my body. It calms him down to have contact. He always throws a small fit whenever I’ve had to pick him up, but those thunderclouds are instantly gone when I give him a raisin. Drama queen

5 days isn’t a long time. Some bunnies take weeks and months to warm up to a new environment

She may not like pets for now and you trying to do so may have already scared her. I’m sure she is curious (going to the door and sniffing the outside is a sign of this), but due to unfamiliarity she’s not quite sure yet. There are a few things you can do:

1) Scatter some pellets or her favourite treats outside the cage, then gently pick her up and put her near the treats immediately. This would help her associate the outside of the cage as being a good/positive area to be in instead of some scary unknown territory. Personally I closed the cage door while doing this so that my bunny couldn’t run back to the cage, but I did put down some cardboard boxes outside in case he really wanted somewhere to hide. If your bunny is extremely prone to stress then I would not go for this option and just wait till she is comfortable to come out herself though.

2) Try not to pet her or touch her. Just sit in the area and allow her to come and sniff or explore you. Once she realises you’re not a threat, she will automatically act more relaxed around you.