If she isn't riding the tricycle because she thinks it's too hard she certainly won't ride a bike that it is impossible for her to ride without someone out helping her until she learns to feel the balance.
Kids start on trikes then go up to bikes with training wheels so they can build the strength to pedal and learn how to manage the pedaling and stopping and steering. Then if you watch they start riding and neither training wheel is touching, that's when it time to raise them higher or take one off. They have a natural progression.
If you get her a bike without training wheels she will likely not ride the bike and miss out on that adventure. It is going to be too overwhelming to her to have to balance, steer, pedal, learn to stand and do all that too, and pay attention to what is going on around her. It's just too much and I don't think she'll ride it at all without the training wheels.
The 16" girls bikes at Walmart with training wheels are under $100 and are sometimes on sale for much less. They last a couple of years because they just fit into that time/size for a while. At 5 they are the tiniest big large but they soon grow into them and then ride them for a couple of years. My 7 year old still rides her 16" bike but got a 20" for Christmas, it was stolen in the last week or so and she has the old one out again. She is 48" tall and the 16" still is a proper size. Her BMX bike is a 20" and has been a bit too big for her this past season, it will be the ideal size for her for the next year or two.
My 4 year old got a 12" boys bike from Walmart for Christmas and it was obviously too small. The 16" is just a bit too big so we kept the small one but when he stands to pedal and then sits down he consistently sits on the back wheel. Walmart does not return/exchange bikes so we were kind of stuck with it. They did say if it was spotless they might consider it for Christmas exchanges. Walmart does not carry the 14" bikes because kids usually skip them. We have a grand daughter just 11 months younger than him so she'll be getting a bike very soon. The small bike is just teaching h9m the pedaling, standing, steering, watching his environment, learning to stop, etc...then he will get the bigger bike.