First, I'll explain what the numbers in 5w20 and 5w40 mean. The 5 means that the oil will flow at zero celsius the same way a 5-weight oil would. The 20 and 40 mean that the oil will flow like a 20 and 40-weight respectively at engine operating temperature (180-195C usually). The actual viscosity of the oil is therefore the SECOND number. The first number just indicates how resistant it is to cold. Remember that even 50-weight oil is thinner at engine temperature than 0-weight is when cold. As a result, 5w30 and 10w30 are essentially equal unless it's the dead of winter in which case a small difference might exist.
I would be hesitant to use 5w40 if not specified unless it was summertime. All manufacturers specify different weights for different temperatures. Having said that, the Volkswagen Routan (which is just a rebadged Chrysler Town&Country) specifies 5w40 with VW spec 502 00 while Chrysler specifies 5w20 despite them both having the SAME DAMN ENGINE! This is very good evidence that the differences between grades are exaggerated at best and completely disingenuous at worst.
Now, I would NEVER put 20 weight oil in ANY engine. The only reason that 20-weight oil exists is because the US Government fines automakers for going above the CAFE (Corporate Average Fuel Economy) limit. The further they go, the more they are fined. Thinner oils like 0w20 and 5w20 are less protective of vital engine parts but they are also less resistant to motion because of their reduced viscosity.
There were some Ford Mustang enthusiasts in the states that did some tests using two mustangs with 4.6L V8 engines. In one car they used 5w20 and in the other they used 5w30. Their findings were that the Mustang with 5w20 did experience a fuel economy increase of 1% but reduced the total lifetime of the engine by 30%. To me, that's just not worth it.
Keep in mind also that 20-weight oil does NOT EXIST outside of Canada and the USA so if your engine was designed outside of those countries which is essentially all automakers except for Chrysler, Ford and GM (but even they use some European and Japanese engines) then your engine was NOT designed to use a 20-weight oil but at least a 30-weight. The automakers don't mind if your engine dies sooner, it means more auto sales for them. That 1% increase in fuel economy means millions in savings for the automakers with regard to CAFE fines. I even had a head tech at a Hyundai dealership admit it to me. My Veloster gets 5w40 in summer and 5w30 in the other three seasons and it works great
