10 hours AMS layover in May

We did both places in August 2022 and spent more than two hours in the Anne Frank House (more time waiting to enter) and three hours at the Van Gogh museum.

First, you must book your reservation at the Anne Frank House early in the month prior to the month of your visit. Book ASAP or you may not get a reservation. You should not book for entering earlier than 10:30am. If you finish by noon or 12:30, you might have time to see Van Gogh.
Second, you must book the Van Gogh Museum and be back at the airport in time to catch your flight (probably three hours prior).

Third the two places are not close, so you would need to catch a taxi quickly to go to the other. The Anne Frank House is farther from the airport than the museum/

We just got back a week ago. We did both of these in one day with time to spare, so yes you can do it. I would leave the AF House for the latest time slot that you can with your timing. I say that because after you visit there, you will not be in a jovial mood to go do fun stuff in town. You could be at the Van Gogh Museum by about 12:30, and I would leave Amsterdam by 5:30 to get back to the airport. So that leaves you with 5 hours. You need to buy tickets for both ahead of time, and there is no wait to get in with those. Some people lined up long before their time, but you don't need to wait in that line, just show your tickets to the employees and they will send you right in. I would allow 2 hours at AF House. That still leaves you with an hour, which is not enough to toss in a canal cruise or anything, so just go grab a bite on the go and wander.

I think it's possible to do both, though I personally would pick one and enjoy a laid back canal cruise. Here's the itinerary I would follow if trying to do both. I typically bike or trams when in Amsterdam, but I would take Uber or taxi to expedite given your tight timeline. This itinerary is also predicated on being able to get the following time slots at Anne Frank and Van Gogh. You MUST book these in as far advance as possible!

10:20am Arrive at Schiphol
11:30am Lunch near Anne Frank House...for something a little different, try a lahmacun (aka Turkse Pizza) at Effendy. It's about a 5 min walk from AF House. Also some really good traditional dutch cafes like Cafe de Prins or Cafe t'Smalle.
1pm Anne Frank House
3pm Taxi to Van Gogh
3:30pm Van Gogh Museum
5:30pm Taxi to Schiphol

Thanks for the suggestions! So basically we can do both if everything works as planned. Then maybe it is not a good idea considering the what ifs that can happen during traveling.

@blakeweathers, thanks for the food suggestions. I'll check those out.

As you noted, it's possible if everything goes to plan - e.g., your flight is on time, you clear AMS immigration quickly (not a given, you can check the business of the airport on your travel day here), you find and operate the airport luggage lockers easily, there are no traffic delays if you take an Uber, and you have no delays repeating the process back to the airport. I myself would choose one of the options and consider it a bonus if you have time to walk around town a bit before heading back to the airport. As noted you must get tickets ahead for either venue. I would not do a canal cruise after a long international flight - I did this on an arrival day and basically slept through it because of jet lag.

@CL, that is a great point regarding canal cruise and jet lag! We will probably do one of the two, wander around, and grab some food. Thanks!