Transmission will not shift to a higher gear until around 5,000 RPMs?

First of all, I would recheck the spark plug type and gap. Here is a guide and the type and specs below:

https://www.2carpros.com/articles/how-to-change-spark-plugs

SPARK PLUG APPLICATION
This vehicle should be serviced with:
NGK: BKR6E
Nippondenso: K20PR-U
AC: R43XLS

Gap 0.71 mm (0.028 in)

Torque 28 Nm (21 lb-ft)

If the engine still is having trouble let's run the codes.

https://www.2carpros.com/articles/checking-a-service-engine-soon-or-check-engine-light-on-or-flashing

This guide can help as well:

https://www.2carpros.com/articles/engine-idles-too-high


Please go over these guides and report back.

Check the spark plugs and they were correct. Regaped them also. The check engine light is not on.

The idle speed did not change. Haven't checked timing.

Did you move the timing? If not, I don't think that is the problem. Even though the check engine light is not on it still can have a code. In the initial post you said "attempted reset of the idle" how was this done?

Have not changed the timing.

Using some carburetor cleaner, I was spraying around the Idle air control valve and found a leak. Fixed that and saw a video on how to reset it. Disconnected battery for about half an hour, then started car and let idle for 2 min in park, 2 min in drive and 2 min in drive with air conditioner on high. After doing that the trouble with the transmission started.

Yep, that is correct, we need to run the codes, let me know what comes up.

No codes came up, but it only checked for stored codes. Is there another diagnostic check that can be done?

Okay, it sounds like we need to check all fuses with the key on. Here are the wiring diagrams for the transmission which show you have a VSS sensor inside the instrument cluster. Does the speedometer work?

Yes.

Tachometer also works.

Let's try removing the transmission control module to check the electrical connector for corrosion, this will through off the values of the sensors and make it shift strangely. Check the image from below to see the location of the module.

Could this be the module? The one wrapped in gray material.

I have a 3-speed transmission. People on the Facebook page says 3 speed does not have a controller.

Can you forward the facebook page please?

Here are some screenshots of the post.

https://www.facebook.com/groups/1034172440036442/permalink/5601865699933737/?app=fbl

Thank you, the guy said there is a three speed, but I do not show one for 1996 but in 1995 they do not show one so it could be a late 1995. How does the power of the engine seem, could you have a clogged cat causing the vacuum to be low therefore holding the gears longer because the computer thinks it is under load?

This guide can help:

https://www.2carpros.com/articles/how-to-test-a-catalytic-converter

Please go over this guide and report back.