Pisa in a few hours in the evening?

Try another computer or device. I can see the calendar for this date and they have bookings until 7:30 pm every 15 minutes.
I would aim for as close to 4 as possible. Not sure how long it takes to climb, or whether you can climb promptly at the time of your ticket, but if open until 10, but only selling entry tickets until 7:30, that might be telling you something. I went long ago when internet was new so there were 2 hour line ups. I climbed the Baptistry and took a photo of the tower from the cupola. Got to hear the guide singing a capella to show the Baptistry acoustics. Brought tears to my eyes it was so beautiful. I think it was a more lasting memory that if I had been in the plodding line up the tower and out. I also recall dinner was 4 scoops of gelato that day - I couldn't decide on fewer flavours.

Try another computer or device. I can see the calendar for this date and they have bookings until 7:30 pm every 15 minutes.
I would aim for as close to 4 as possible. Not sure how long it takes to climb, or whether you can climb promptly at the time of your ticket, but if open until 10, but only selling entry tickets until 7:30, that might be telling you something. I went long ago when internet was new so there were 2 hour line ups. I climbed the Baptistry and took a photo of the tower from the cupola. Got to hear the guide singing a capella to show the Baptistry acoustics. Brought tears to my eyes it was so beautiful. I think it was a more lasting memory that if I had been in the plodding line up the tower and out. I also recall dinner was 4 scoops of gelato that day - I couldn't decide on fewer flavours.

Thanks Maria. I was on Chrome earlier. When I use Safari, I can see the dates. When you say "aim for as close to 4 as possible," do you mean aim to get in to Pisa at 4 or buy the ticket for 4? If the latter, what is special about 4?

Do you recommend climbing the Bapistry as well? Not sure hong long my trip will increase if I add that?

It looks like sunset in Pisa is around 9PM, so I think I'd get to watch the sunset.

The baggage drop at Pisa Centrale is near the end of Platform 1, to the right facing the station.

Sorry, meant at the least, arrive in Pisa by 4. Depending, some may find Baptistry hokum. If you can get in without repurchasing tickets, keep it in mind

If you plan to check luggage and walk between the train station and the Field of Miracles, plan on about 1.5 hours for just those activities. I'd suggest arriving by 4pm, checking your bags and heading straight to the Field of Miracles. When you finish will determine how leisurely you can be in returning to the station area. It might be best to look for a dinner spot reasonably close to the station, and it will probably need be a somewhat short dinner if you're to catch your 8:51pm train. Five hours in Pisa might sound like a lot of time, but it will go quickly with all you have planned.

Got it, thanks.

I'm not sure that I need to check luggage. I think I'll only be traveling with a laptop backpack and a small string bag. I think I could just carry that with me.

It actually looks like the Tower has a gap between 3-6PM where no tickets can be purchased. Either that, or it just so happens that all of those times have been booked for the entire month of July, and every other time slot is not fully booked.

Edit to above:
The link that I pasted previously http://www.towerofpisa.org seems to not actually be the main website.
The main website is https://www.opapisa.it/, which doesn't change the 10.00 booking fee that the above site charges.

I think it's enough time to do what you list. We were there in October on a day-long bus tour and arrived around 4:30. We were there a couple hours at most and had time to take pictures holding up the tower and walk around the town. Everything is really close by and, with the time you have, you should be able to climb the tower (if you can get a ticket), tour the Baptistry and Cathedral and have dinner at one of the nearby restaurants. There were people on our tour who climbed the tower and they had plenty of time. Even though we were there a very short time, I thought it was so worth seeing the tower and we really had fun watching and joining the many people taking pictures holding up the tower!