Ok. You said you apply steady 5V to the input but how did you get 0V on the input? To get a fast transition logic 1 to 0 time by just touching the input with a clip-lead you will need to add a pull-down resistor to ground (say 1-10kΩ) and it doesn't sound like you have that. If the input is floating when you remove the 5V from the input, than the input is undefined and the output can be erratic. In your case it apparently slowly floats toward ground which would account for the slow output rise to 5V.
The rule with CMOS is: NEVER LEAVE AN INPUT FLOATING, unless you want random behavior from the chip. It's a simple rule but many working with CMOS seen not to know it.
Yes, the ouija comment was my attempt at a little humor.