Your sr5 if its standard came with the c50 stock like eage8 said. All c series axles will swap over to any other c series. your swap most likely came with the drivers side axle cut or the shaft was taken out of the cup that goes into the transmission.
All silvertop and blacktop equipped cars came with equal length passenger side axle. So they probably left the part bolted to the block and again took out the rest of it that bolts into the steering knuckle.
Your options are use another drivers side axle and use it on the passenger side so you still maintain the equal length axle or use your stock unequal length axle from the sr5.
Here is a picture of what your should look like, just tell the shop they can use a drivers side in the cup for the passenger side. If its damaged or not useable just put in your sr5 axle.
I edit because if anyone else is reading this I'm not sure if lsd equipped c-160s will take a regular c series axle or if its specific to that trans
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