5-10C but wet is easy mode. Use a rain jacket, rain pants, and rain spats (optional). It's harder when it's warm and wet, as you can choose between getting wet from the rain, or sweating under your waterproof gear.

Warm and wet is easy because I just change clothes at work. There's a shower at my office.

Personally I use acceptance ;) Which I think is an important ingredient that most Dutch citizens learn as they start cycling to high school regardless of weather: it won't always be pleasant. In the rain I'll get wet, no biggy. At work I won't be the only one putting a coat and shoes on the heater to dry. Some discomfort is present in all modes of transport, this is the one I chose to put up with.

I also use a raincoat with cap and rain pants, which should fall over your shoes. However, I only use this in heavy rain, because with light rain I get wet anyway from my own sweat (wet rain gear usually does not breathe enough for me).

Then there is the rain radar [1], but is probably not available for your locale ;)

[1] https://buienradar.nl

Right, it was 19 miles to bike from my house to my HS, which is a bit far, and long enough that a bus was faster (though at least most of it was separated from automobile traffic).

Rain pants. I was a mormon missionary in northern Japan, and we rode mountain bikes everywhere, regardless of weather. Typhoons, blizzards, compacted ice and snow on the ground, all of it is actually quite easy to bike in. Assuming you already have a water proof jacket, about $30 is all you need to get some waterproof pants that can quickly be pulled over your actual pants and keeps you perfectly dry, and then removed at your destination.

Weather should really be one of the least concerns on anyone's list for cycling.

I find that it's not actual rain that's the problem, but the risk of rain. I hardly every get wet on my commute, but if it says 60-70% chance of precipitation, then that may prevent some people.

I find it handy to simply have a pannier with my rain gear:

* https://www.rei.com/c/cycling-jackets

* https://www.rei.com/c/cycling-tights-and-pants

It's not heavy, though a bit bulky, and if it does actually start coming down, one can just pull over and put it over one's regular clothes. If you can, try to ensure that whatever over-gear you get says "breathable": wearing the equivalent of a garbage bag reduces comfort.

I personally wear the funny-looking cycle attire as well, but that's because I like to pedal hard to get some cardio (instead of going to the gym). If you pedal at a slower pace then you may not work up a sweat--at least not after ~2 weeks once you're in better shape.

Cycling pants. You shouldn't have too much trouble finding waterproof pants to go with your jacket. There are some that fit over other clothes (which also provide a lot of insulation if it's cold) and some you wear as if they were regular pants. You can also get shoe covers.

The German military has some literal pullover pant+jacket rain combo. It is quite robust woven nylon on the outside with PTFE membrane below (shielded from the inner garments with thin woven PET). You need gloves to prevent moisture wicking up, and might have to get creative around the face/hood/chin border, but otherwise this (I'd suggest a civil clone; the original seems to only exist in Flecktarn) should do the trick. And it's highly breathable.

Rain pants? Pretty standard here in Copenhagen. It helps if it's coldish, otherwise you either sweat more or cycle slower.

A change of shoes and socks can also be appreciated if it's tipping it down.