If you are worried about your hoses, just wait till the system is cool and given them a squeeze, If they are crunchy then a swap is a good idea, if not too bad and still a little soft then they should be fine.
Anyway the small hose is no biggie. After 15 years all the hoses can become brittle and can burst. Usually it's the main radiator hoses, but any can go at any time. You will need to get one of these from Mazda, and if you have basic tool skills can do it yourself.
When the car is COLD!!!! drain the fluid from the bottom of the radiator (there is a small Phillips head screw), use rubber gloves if you have some. It is toxic so don't get it in your mouth or eyes. Drain into a tray, will be about 4 litres in there. Remove the radiator cap to make it come out quicker. It's good to replace the fluid every couple of years anyway.
Use pliers or vice grips to squeeze the little metal clamp back at each end of the hose. And pull them back along the hose.
The hoses often rust on so you may need to use pliers, a knife or screw driver to get the old hose off with a bit of wiggling and twisting.
Stick the new hose on (with the clamps).
Do up the screw on the bottom of the radiator and refill the system with coolant. Check the coolant after a day (only when car is COLD).
Hose should be only $25 or so at a guess, but Mazda is Mazda

and if you don't want to do it yourself I'd say it's a 30-45 minute job for a half decent mechanic and an hour for a Mazda specialist
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