Transmission shift solenoids

Metal inside the transmission is not a good thing. Shift solenoids don't get clogged unless there is some debris (like metal shavings) floating in the fluid.
The shift solenoids are all inside the transmission. BUT from your description try this test first, Shift into low gear manually. Now shift up one gear at a time. Does the trans still jerk hard when going into 3rd gear? If it does it likely has internal damage and not an electrical issue.

I am not sure which solenoid in my transmission that needs to be replaced. when starting to drive and shift into drive it takes about 45 seconds before it engages into drive gear. I also have no fifth gear, cannot take it over 55 mph. Any ideas?

Is the check engine light on? If it is a solenoid, it will code.

https://www.2carpros.com/articles/automatic-transmission-problems

When was the last time you change the fluid and filter?

https://www.2carpros.com/articles/how-to-service-an-automatic-transmission

I attached the procedure for the pressure regulating solenoid. This could be your issue. The procedure with pictures are below.

Can you please tell me how to replace a solenoid?

You will need to drop the pan and the solenoids are in the valve body. You will need to raise the car safely here is a guide for that.

https://www.2carpros.com/articles/jack-up-and-lift-your-car-safely

This help help pull the pan and service the transmission

https://www.2carpros.com/articles/how-to-service-an-automatic-transmission

Here are some diagrams below showing you how to do the job.

Please let us know what happens.

Cheers, Ken

I have these codes on my car:
DTC P0762 4-5 Shift Solenoid (SS) Valve Performance - No Fifth Gear
DTC P0700 Transmission Control Module (TCM) Requested MIL Illumination
DTC C1244 Powertrain Indicated Engine Drag Control Malfunction
DTC P0171 or P0174 Fuel Trim System Lean

I need to know if I can do the solenoid myself. Someone else is telling me I have to drop the transmission and send it out to California to get worked on and then have it shipped back out here.
I also have no idea what Powertrain Indicated Engine Drag Control Malfunction means. I have looked online and am not sure what is causing this or what it means.
Any help would be very much appreciated. Thank you.

Trouble codes are given in the order of importance so if you fix the solenoid the rest will probably go away. You can do the work yourself by removing the transmission pan this guide should help.

https://www.2carpros.com/articles/how-to-service-an-automatic-transmission

Here are diagrams to show you how to replace the 4-5 shift solenoid - below

Check out the diagrams (below). Please let us know what you find. We are interested to see what it is.

Cheers, Ken