What types of jackets do I need in May?

I always go to Wikipedia and pull up the cities I'm visiting. They have a chart showing average high and low temperatures month by month, precipitation days, etc. Then you can make an informed decision.
Many mountain places see a lot of rain in April and May, and temps can vary. And many days are glorious that month.

I suggest taking a packable down jacket or at the very least a fleece jacket that can be layered with your rain jacket. If you are in higher elevations it could get chilly.

I travel in Switzerland in late May often. I bring a light weight rain jacket, nothing heavy. Layer for warmth. If you run into a cold spell, buy a jacket there.

I have not been to Switzerland, but I often travel March through May, and have been far north in Sweden during that period. I live in New England so I always want it colder than it really is when I travel. I checked the general temps for a comparison. It seems generally it will be pretty warm from my perspective. Layers is always the solution when traveling. I would suggest getting a down-type vest that folds up very small, which you could wear under your raincoat should it be really cold. The vest could layer over a sweater or fleece type sweatshirt, whatever you want to pack for that light layer over a teeshirt or blouse. I also pack leather gloves, not heavily lined, and something to cover my ears, like a headband, should it be unusually cold or wet (particularly the gloves). So really, all you need is to include a vest, gloves, and headband so really not too much more. I would pack both long-sleeved and short sleeved tees. It is all about layering.

I don't consider average temperatures very helpful in this sort of situation. I like to look at the actual, day-by-day historical temperatures in recent years. It's the extremes you might need to cope with, not just the averages. Such information is available on timeanddate.com. I've linked to the May 2019 data for Lauterbrunnen, but I see that for Switzerland the website also has stats for some higher elevations.

This website has useful information on how much temperatures drop as elevation increases.

Back in the 1970s and early 1980s I traveled around Switzerland several times after Memorial Day. I was often chilly in June at lower elevations. Even 50F can be unpleasant if you get wet. I don't know whether there's more or less risk of cold weather these days.

In 2018 I needed merino long johns, a light fleece jacket and a rain jacket to be comfortable on wet, 40F mornings. I didn't have rain pants, but my nylon PrAna slacks over the long johns some how kept me dry. I was not outdoors in all-day rain, but I got caught twice in heavy downpours. That was in early April in northern Andalucía, not at altitude.

Being able to layer is more important than a single solution garment. I live at 7,000 feet and in the spring and fall see big swings in the temp thru the day. Right now I'm a big fan of 32 Degree base layer tees ( they come long and short sleeve, sink wash/dry overnigth), a fleece quarter zip pullover or jacket, and a roomy jacket that's at least wind and rain resistant.

You can go to Google and search for weather for the places you are going, just type location and weather. Then dress appropriately for the temperatures shown. Do not use peoples descriptions of what they wore because everyone has a different tolerance for temperatures. We H]ave been to Lauterbrunnen numerous times in May and September and been perfectly comfortable with light jackets. However if you go up to the Schilthorn, you will find the mid to low 30s and you will want a lot more. The best solution is to dress in layers. For example my wife found that her ever on hand nylon rain coat over her other jacket worked OK on the Schilthorn.

While there is day to day variation from average temperatures a general rule of thumb is that the higher the altitude, the more stable the temperature.

We were in Switzerland last year mid-May. As someone above mentioned, layering is good. I had a light rain jacket with hood, a light fleece jacket, a sweater and a light long sleeve shirt. I wore all of these the days we went up the Schilthorn and to the Jungfrau. I also had a scarf, hat and gloves to wear as needed. I was never cold.

Wow thank you all so much for the many replies and resources! I think the layering of jackets is the way to go. Thanks again!

Im traveling in early May- and this info was very helpful. Thanks everyone😊