If you caused the damage to the vehicle then yes you would be liable and can be held responsible. You did the right thing by leaving your information on the vehicle. Most state laws require this if you are unable to find the owner of the vehicle to inform them in person of the damage caused.
Some states also require you to make a police or accident report in a certain amount of time if the damage is over a certain dollar amount so you may need to check with the DMV to see if this is necessary.
The time limitations a person has to report an accident to an insurance company or get an estimate vary from state to state but it is normally longer than 5 days. Since it was a parked car that you hit, it could be that the person was out of town or did not see the damage or your note for 5 days. In most states the person has about 2 years to take you to court if the damages are not taken care of through an insurance claim and they decide to go after you personally.
Since you damaged the parked car, the person can inform their insurance company but in most states they would put in the claim through your property damage liability policy. If you have given them the information to do so and they have not yet contacted your provider, then your insurance company may need to contact the person so that the damage can be looked at by the claims adjuster or the person can be told where to go to get an estimate on the repair costs.