I cleaned the battery terminals and connectors, the lug on the red cable was corroded and broke off so replaced that. Also added water to two battery cells that were a little low but not significant. Got a new volt meter and the battery reads 13V when mower is off and same when it is running. Both fuses near the battery and the ignition switch are fine. Jumped it again, and it runs fine for about 5 mins, then stops running, there is little back-fire when the engine stops, and then I get nothing when I turn the key to restart. Charging system issue?
It's possible that you may have more than one problem going on here. The stopping after 5 minutes *could* indicate a plugged gas cap vent (perhaps from a mud wasp or whatever, causes a partial vacuum to form in gas line cutting off fuel supply). *Could* also be a magneto overheating causing system to fail or the diode is opening after 5 minutes allowing the magneto to go to ground.
To me, as the engine backfires when it dies indicates an electrical problems the cause. The most logical cause is related to magneto failure or the magneto kill circuit being activated by a failure of some component.
If the engine dies after 5 minutes and *everything is dead* (no crank, no lights, etc), that indicates only one thing may be at fault.
However, if the engine dies after 5 minutes and the *battery is dead* (will start after jumping), you possibly may have more than one problem (as the engine does not need the battery to continue running as the ignition is derived from the magneto.) One component is causing the engine to die, a second causing the battery not to be recharged.
Looking at the electrical schematic for a 915031 (guessing that it's similar to your ZT), when you turn the key to start, power comes from the battery through a heavy red wire, runs through the 25 amp fuse to the B terminal of the ignition switch (IG).
Out of the A terminal of the IG switch to a connection point where the regulator and seat switch connects.
A purple wire continues on to term #1 of the PTO switch. Comes out on term #7 & runs to term #1 of the parking brake, out on term #2 to S2 of the IG switch. Out on S1 of IG switch to starter solenoid, completing circuit and engaging starter.
Looking at connection where the regulator and seat switch connect. This will be at the seat switch itself. Power goes into the seat switch at the #1 terminal, out of the #2 term on a red/yel wire to term #1 of the parking brake switch. Out on term #2 on a yellow/red wire to to the starter relay, terminal #86. Out of relay coil on term #85 to ground (actually to ground fuse terminal A, then to ground).
The starter relay must remain energized throughout the operating cycle, and should it fail to hold, it would allow the magneto to go to ground, killing the engine. It's held on by the seat switch and the parking brake switch. Could be the problem for engine dieing, but would not be the cause of the battery not charging.
There's also a diode coming off the relay, should it open in service, it would prevent the engine from cranking.
Analyzing all this, the only part that is common to everything you describe is the 25 amp fuse coming off the battery. I believe I would start by replacing both 25 amp fuses (both battery fuse and ground path fuse) to eliminate this possibility, and it's a cheap test. There's a slight possibility that one of the fuses is damaged and failing when it gets hot.
A damaged battery or charging system would not (should not) account for the engine dying after 5 minutes of running. Sounds like electrical component failure due to heating up. When it gets so hot, it opens and kills the engine through the magneto kill circuit (just guessing).
Does the engine crank after it dies? If it does, I would suspect two problems. One causing the engine to die, one not allowing battery to charge. I would suspect starter relay or diode (causing magneto ground circuit to activate), and/or the ignition switch.
If it does not (switch set to run position and headlights don't work), it points to the + fuse opening when hot (most common item,) or failure of the ignition switch. (Burned contacts offer less contact area when running and will get hotter then normal. Could be hot enough to open during use, breaking the circuit. (Not unheard of).