your internet speed has nothing to do with your local area network speed
what is your internet speed connection, the contract you got with your isp?
if it is 5 megabits per second, then speedtest just confirmed that
wifi or ethernet will depend on that speed
a good wifi can go up to 500megabits per second, a good ethernet will go up to 1000 megabits per second
a good internet connection, for home, can be on most places 100 megabits but most times is very expensive
the outer or the network depends on how much you pay for that contracted internet connection and will limit themselves to that limit