Ok. In that case, I'd position a paid pilot for 100 users to prove out the value/ROI at some rate that's less than the cost of the existing tools. This should be within VP discretion and won't trigger a procurement process. Once the ROI is clear, then you can negotiate a larger deal. Rolling any software out for 5K people especially if it includes replacing tools is a large undertaking for a company.

You should expect it to take at least a year. There are other contracts they will have to get out of. There is data in those systems that will need to be dealt with.