Can anyone give an idea on how to determine what the maximum amperage the secondary winding of a step down transformer would be, without over heating it?

The primary winding is (120vac) 126.7 ohms. The secondary winding (12vac) is 5.7 ohms. Any idea how many amps can be loaded on the transformer without causing it to heat excessively?

Here's what I'm up to....I have several strings of 5 halogen light the previous owner installed under the cabinets in the kitchen. 2 of the transformers burned out (open windings). Each string of lights draws 5 amps at 12vac. The cost to replace the transformers is just about the same as to replace the lights. I have a couple of salvaged transformers from other electronic equipment with 12vac outputs. Of course, there are no nomenclatures stamped on those to indicatemax. amps output. I'd like to use one of them to run 2 or 3 sets of the lights which will be 10-15 amps 12vac. I plan to put 5 amp fuses on each lead of each string of 5 lights. Again, each string contains 5 10 watt halogen bulbs.

Thanks in advance to any guru's who can show me the math to figure maximum amp capability on the secondary winding.