You will see a red key warning light if fob battery is low (among other conditions). You can still start car by pressing and holding start button. There is no blade key hidden in fob. Iirc salesman said there*s some fob power stored but get battery replaced ASAP.
Pretty cool interactive online owner*s manual. Much easier to navigate than book.
http://owners-manual.mazda.com/gen/en/cx-5/cx-5_8gj1ee18b/visual.html
Under the following conditions, the KEY warning light (red) flashes after the push button start is pressed. This informs the driver that the push button start will not switch to ACC, even if it is pressed from off (for vehicles with a type A instrument cluster (Search), messages are displayed in the instrument cluster).
The key battery is dead.
The key is out of operational range.
The key is placed in areas where it is difficult for the system to detect the signal (Search).
A key from another manufacturer similar to the key is in the operational range.
(Forced engine starting method)
If the KEY warning light (red) illuminates, or the push button start indicator light (amber) flashes, this could indicate that the engine may not start using the usual starting method (for vehicles with a type A instrument cluster (Search), messages are displayed in the instrument cluster). Have your vehicle inspected at an expert repairer, we recommend an Authorised Mazda Repairer as soon as possible. If this occurs, the engine can be force-started. Press and hold the push button start until the engine starts. Other procedures necessary for starting the engine, such as having the key in the cabin, and depressing the clutch pedal (manual transaxle) or the brake pedal (automatic transaxle) are required.
When the engine is force-started, the KEY warning light (red) (if equipped) remains illuminated and the push button start indicator light (amber) remains flashing.
(Automatic transaxle)
When the selector lever is in the neutral (N) position, the KEY indicator light (green) (if equipped) and the push button start indicator light (green) do not illuminate.
http://owners-manual.mazda.com/gen/en/cx-5/cx-5_8gj1ee18b/contents/05010200.html