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Do not mix the 2 weights. If you have already, don't worry about it. Just do not make a habit of mixing grades or weights.
You are good to go with the 10w-30. The real important thing is proper oil changes. I would not go synthetic if not specified by Honda. Especially if high mileage.
5w30 vs 10w30 – Differences in Engine Oil Viscosity
What’s the difference between 5w30 and 10w30 oil? These oils are different thicknesses in cold temperatures with 5w30 being the thinner of the two.For this reason, it’s recommended to use it instead of 10w30 for vehicles operating in cold climates.
The first number, 5 or 10 in this case, is a measurement of how easily the oil pours at low temperatures.
The lower the number, the thinner it will be in these conditions: a 0 pours easier than a 5, a 5 easier than a 10, etc.
An oil with a lower viscosity (a lower number) will reach and protect the engine’s internal components faster.
The second number, which is 30 for both of these oils, indicates the thickness of the oil once it reaches operating/high temperatures.
A high viscosity (thicker) oil will adhere to mechanical components better when subjected to high pressure and stress and can withstand higher temperatures
before thinning out beyond its working viscosity (past which it can no longer provide adequate protection).
When to Use 10w30 vs 5w30
The only difference between these two oils is cold flow ability: a 10w30 oil will move slower than a 5w30 oil during cold startups.
At operating temperatures, both oils will have the same viscosity (30) and will flow and protect identically.
If the oil will be in the engine during winter and you live in a place where it gets cold during these months, use 5w30 oil. If it will only be in the engine during the summer, use 10w-30.
If you live in a tropical area where temperatures are consistently high and it never gets near freezing, an even higher starting viscosity oil like 15w40 can be used.
You should always use the weight of oil recommended by your vehicle’s manufacturer to provide your engine with the best protection and maximum fuel economy.
Using an oil with a viscosity that is too high can result in excessive oil temperatures and increased drag, while using an oil with a viscosity that is too low can cause that oil to fly off of internal components when they’re in motion, leading to metal-to-metal contact that will accelerate engine wear. That said, most automakers will specify a range of oils that can be used in their motors, letting you choose the best viscosity to fit your driving conditions.