10 years AC, 5 year Furnace, right?5 years.
You do not need to change the furnace as it should be high eff, +95%.
With the funding, you can just replcae the AC with a heat pump. Whether or not you are going to use the heat pump for heat, you are still saving money!!
You only need to spend a little for a more effecienct AC (heat pump).
If you are using heat pump for heat, just setup the transfer temperature not lower than -5 or may be just at 0. Below that temperature, you will use your 5 year old effecient furnace for heat.