It depends a lot on you.
I live in Illinois and I'll go out in a T-shirt and shorts in the 40's for bike rides.
But if you want some additional warmth in the around 40F and 3 miles, I'd say maybe some thin gloves (I have a set of Underarmour coldgear running gloves which are useful for longer rides in the 30s) and a hoodie - you might be cold for the first 2-3 minutes
but then you'll feel fine.
If you find that a hoodie leaves you cold for the whole ride, maybe add a wind breaker with some ventilating holes.
In general, you shouldn't dress enough to feel warm when you're getting on the bike.
You'll generate some extra heat, so in most cases, the right amount of clothing will make you feel a bit cold for the first few minutes.
A ski jacket is way too much bundling for riding in 40 degree weather (given that its probably overkill for even just standing outside).
bicycles.stackexchange.com/users/8219/Batman
I find that at warmish cold temperatures like the 30s-40sF, the most important thing is to keep my hands and ears warm; the rest of my body takes care of itself after a few minutes of riding.
(I am assuming your normal garb does not leave exposed skin other than hands and head/neck.
If it does, well, fix that first.)
Have a good pair of wind-stopping gloves; experiment with glove liners if the gloves aren't enough.
A fleece earband keeps my ears and forehead warm and doesn't get in the way of my helmet, but if that's not enough or your nose complains, try a hoodie, stocking cap, or balaclava.
You may find that keeping the wind from stripping heat away is plenty enough for the rest of your body, in which case a standard rain jacket or nylon windstopper will do the job.
If it doesn't, try a hoodie or put on a fleece vest or jacket under the rain jacket.
(A water-resistant jacket with fleece lining is essentially this; Land's End carries such, among others.)
Other minor considerations:
Sleeves that are snug at the wrist (e.g. stretchy knit cuffs or buttoned cuffs) keep the wind from sneaking up your forearm.
Crew or longer socks do the same for your ankles and calves, or failing that, a cycling cuff-band.
bicycles.stackexchange.com/users/3631/D.Salo
I've found that "soft shell" garments work really well in that temperature range as long as it's not raining.
Soft shell fabrics are jack of all trades.
They are much more breathable than your typical nylon shell, they are more windproof than a microfleece and with a good DWR
they are reasonably good at repelling light rain and snow.
My favorite fabric of this type is Schoeller Dryskin, but it's kind of pricy.
Polartec Powershell also works pretty well.
IMHO, you want to avoid anything that claims to be waterproof/breathable.
Even the best versions of these kinds of fabrics are not breathable enough for moderate exercise.
WB fabrics (i.e. goretex) have their use, but they are vastly oversold.
bicycles.stackexchange.com/users/8445/Fred the Magic Wonder Dog
My commute has always been about that distance, and when temperatures reach around freezing point, I simply wear a ski jacket which has ventilation shafts under the armpits.
Opening these helps me a lot from sweating, and you can easily adjust them.
Also thin (e.g. running) gloves can help: they break the cold wind, but allow you to transpire.
And finally, like in warm weather: don't rush too much.
bicycles.stackexchange.com/users/7161/Jaap Eldering
5 degrees celsiusis is chilly and the main enemy is wind.
Those are the areas of the body, that generate a excessive heat: torso head thigh
Those are the areas, mostly affected by wind:
knees palms front part of the body: breasts, neck, face
I would wear:
no backpack knee pads, thin gloves wool shirt with long sleeves helmet
In colder weather (below freezing) I would add: wind breaker winter gloves ski mask
long trousers At below
-20C
I would add: ski jacket ;p
bicycles.stackexchange.com/users/3927/Vorac
I bought a few wool blend base layer tops and bottoms and a pair of neoprene gloves, all from Costco, which keep me very comfortable down to 40 degrees.
As the temperature dips lower, I am experimenting with adding layers.
At 34 degrees, I wore two pairs of the base layer bottoms, one on top, plus a very thin windbreaker from REI, which worked very well.
I commute about 10 miles each way.
bicycles.stackexchange.com/users/13786/Neil
I bike to work. It's about 3 miles. I live in Minnesota. It is getting cold. When it is like 40 and below I bundle up but I sweat  and then I am hot so I lose a layer and then freeze. Should I wear like a windbreaker or that under armor stuff? I get to work and my body can not tell if its freezing or sweating.
How to dress for biking 3 miles to work in 40°F (3°C) and below so not to sweat to much but still keep warm
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<winter><clothes>
bicycles.stackexchange.com/questions/25080
bicycles.stackexchange.com/users/14052/William Runyon
Biking will make you feel warmer so the right amount of clothing is what you feel slightly cold in at the beginning of the ride. A windproof jacket with ventilation is a good idea. Gloves are probably required and maybe something to cover the ears. Wool base layer tops and bottoms are also recommended.  This depends on your tolerance to cold weather, but generally you should dress so you don't feel warm for the first few minutes of your ride, to avoid overheating later. If you are too cold at the end of the ride, wear another layer next time. A ski jacket may be too warm, but a light windbreaker or tight sleeves can stop the wind from reaching your skin. Keep your hands, ears and forehead warm with thin gloves and a hoodie, balaclava, ski mask or stocking cap. A windbreaker with ventilation can protect against the wind. Softshell can be better than 'breathable' waterproof jackets, which are often not as breathable as advertised.
This depends on your tolerance to cold weather, but generally you should dress so you don't feel warm for the first few minutes of your ride, to avoid overheating later. If you are too cold at the end of the ride, wear another layer next time. A ski jacket may be too warm, but a light windbreaker or tight sleeves can stop the wind from reaching your skin. Keep your hands, ears and forehead warm with thin gloves and a hoodie, balaclava, ski mask or stocking cap A windbreaker with ventilation can protect against the wind. Softshell can be better than 'breathable' waterproof jackets, which are often not as breathable as advertised.