May is an unpredictable month, weather-wise. As a solo traveller, I'd pick the rain jacket, for the following reasons:
1. Hands-free travel. You can look at your phone for directions without juggling an umbrella.
2. Maybe I'm a weakling, but I hate carrying an umbrella for any length of time. It's heavy, easy to bump into other people, opening and closing it and then stowing it when going into shops is horrrid. And if it doesn't rain, it feels like it weighs 5 pounds in my suitcase.
3. Rain jacket is multi-purpose. It's a good idea to travel with a light jacket, might as well make it a waterproof, breathable rain jacket.
To the people who say that people will look at OP weird for wearing a jacket in Europe in May--No. The weirdos are the American tourists wearing sundresses and shorts in Rome when it's 75 degrees. All the Romans are wearing scarves and light jackets and boots, lol.