My guess is that this is rooted in your placing the primary windings in parallel, something that requires careful consideration.
I believe in general the ratio between paralleled windings must be 1 (otherwise you'll get huge currents, limited only by the internal winding resistance). This is presumably what you're trying to do by specifying turns as 5 and 5. However, now it is becomes a simulation issue as the simulator effectively sees this as two voltage sources in parallel. Even though the voltage sources have the same value, the simulator unfortunately cannot deal with this scenario and reports singular matrix errors (see error log)
The best way to deal with this is simply to small series resistors to the coils. This would a reasonable characteristic anyway for any practical transformer. This can be done externally or from the Resistance tab in the transformer.
I beleive you are correct, and I found an easy way to add resistance to the coils. Simply double clicking on the transformer brings up a new window where the a variety of parameters including the coil resistance can be changed. I chose Symmetric resistance and the default 10m ohm and the simulation works.