Our tstat is set at 72 and the other night it got down into the mid 30's. When the heat first comes on the air coming out of the register is very cool (around 75) and then after running for about 5 minutes the temp at the register finally reaches the mid 90's. Is this normal heat pump operation? Does it usually take several minutes to reach the max temp at the registers?

Furnaces have a delay to prevent that. For reasons I don't know, heat pumps don't.

Regarding your heat pump. That's exactly the way mine works, the fan comes on when the thermostat calls for heat, and it takes a while for the heat to actually arrive. Gas furnaces usually build up heat first before the fan comes on, while heat pumps just blow whatever air happens to be in the ducts. As long as you have heat, the pump is working.

If you have a gas furnace and want to solve this problem by turning on the gas furnace earlier you can change a setting in the heat pump. Most so called dual fuel heat pumps will not run after the outside temp gets below 40 degrees F.