We need some more information… Most likely, you will need to tie the GND on the Arduino to the GND on the existing security panel. This will then allow both systems to have a common reference voltage. Again, please be sure the voltages are both 5V DC TTL level before connecting the two systems together. If the old alarm is running at 12V or 24V DC (or AC!!!) then you’re going to need to build a circuit similar to what Ken Washington showed earlier.
When you say you’re measuring +5v and +2.5v, we need to know exactly where you have you voltmeter leads attached. Is this completely at the old alarm panel? Or are you measuring voltages at the Arduino?
NOTE: Do NOT connect both the Arduino +5V and GND to the old Alarm Panel. You should only connect the GND on both systems together. If you were to connect both +5V and GND between both systems, you will start flowing current between the two power supplies, as there is no way both systems are at the exact same voltage. (If the old security system does have a decent +5VDC power source, you could actually use it to power the Arduino. In that case, you would remove the dedicated Arduino power supply altogether.)