Solution-processed semiconductor quantum dot solar cells offer a path towards both reduced fabrication cost and higher efficiency enabled by novel processes such as hot-electron extraction and carrier multiplication. Here we use a new class of low-cost, low-toxicity CuInSexS2-x quantum dots to demonstrate sensitized solar cells with certified efficiencies exceeding 5%. Among other material and device design improvements studied, use of a methanol-based polysulfide electrolyte results in a particularly dramatic enhancement in photocurrent and reduced series resistance. Despite the high vapour pressure of methanol, the solar cells are stable for months under ambient conditions, which is much longer than any previously reported quantum dot sensitized solar cell. This study demonstrates the large potential of CuInSexS2-x quantum dots as active materials for the realization of low-cost, robust and efficient photovoltaics as well as a platform for investigating various advanced concepts derived from the unique physics of the nanoscale size regime.