I'll bold the important parts.
12-11-1. Special election to fill congressional vacancy--Time of election of representative. If a vacancy occurs in the office of a senator or representative in the United States Congress it shall be the duty of the Governor within ten days of the occurrence, to issue a proclamation setting the date of and calling for a special election for the purpose of filling such vacancy.
Ok, so what do we know so far? Only that the Governor must, within ten days of a vacancy in either chamber, set a date for the special election.
If either a primary or general election is to be held within six months, an election to fill a vacancy in the office of representative in the United States Congress shall be held in conjunction with that election, otherwise the election shall be held not less than eighty nor more than ninety days after the vacancy occurs.
Nothing about Senators so far. The next several sections aren't relevant.
12-11-5. Special election to fill senate vacancy. The special election to fill the vacancy of a senator shall be held at the same time as the next general election.
Ok, so 12-11-5 is relevant. The special election for a vacant Senate seat will be during the next general election; 12-11-1 simply requires the governor to, within ten days of the vacancy, set the date of the special election to the same day as the next general election. No conflict between the sections at all. One applies to House members; the other, Senators.
-PJ