From a purely theoretical standpoint the only two things I could think of that having a oil that is thicker at starter up would cause are the starter would have to work harder to crank the engine and the oil pump would have to work harder to get the oil moving. That could affect longevity of the starter from the higher load. It could lead to accelerated wear of bearings from lack of oil at startup. Unless Vespa has done something very unusual in the design of their engine I don't think the difference between 5W and 10W is likely to cause either unless you are starting the bike in very cold temps.
You will find that you can use a 10-40 oil if you wish. It's listed as ok in the owners manual on all 4 stroke Vespa's for normal ambient temps. But as Buffalo says, it's too thick in sub zero temps so the 5-40 would then be better.
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