Honestly your system is a little weak to play it well. So turn off shadows and other graphics options to see when performance is ok.
Your internet service will not have any effect on the game speed.
Your processor is very old now and the 8600gt will just barely push SH5 but you may be able to get it playable.
There are some bugs in the original version of SH5 that cab be remedied with mods, check out the mods workshop forum and get some mods!!
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