i broken a couple T series axles with a locker. they dont last for ever for sure.. mine due to axle splines wearing out and too much slop. managed to drive home the first time on the other axle, replaced axle and cleaned the head out.. put it back in. second time wasnt so lucky.. it peened the carrier and cracked the side bearing.
your 5speed doesnt really have anything to do with the diff. every car came with different ratio's and diff sizes. you should try get the same size, same ratio diff head as what was originally in your car to keep the speedo in spec (unless you've changed rolling diameter or something).
some things you could do to check for a broken diff without driving it..
jack diff up and sit it on axle stands or sit it on a jumbo trolley jack. let handbrake off.
if its a locker then if you spin one wheel the other one will spin same way without any restriction to movement. they should both spin at same rate.. if not then could have broken axle. if its jamming up then sounds like crown/pinion gears damaged.
if its open diff, other wheel will spin in opposite direction or driveshaft spins but either one should spin in a smooth manner. if not then sounds like spider gears or crown/pinion damaged. if you were to turn driveshaft then both wheels likely to spin same direction (but not always). either way there shouldnt be harsh operation.
replacing the head can be frustrating if you dont know how. especially if the axles dont come out easy and you dont have the correct tools.
put simply.. you need to drain the oil out. take driveshaft off, pull axles out, then lastly unbolt the head and remove it from the housing. that is often a bastard job. dont leave axles sitting in the housing as the weight of em will squash the end seals. also try not sit axle up on the wheel end if they covered in oil as if it seeps into bearing it thins the grease out.
must make sure no metal fragments left inside diff housing.
fitting is opposite of removal but make sure the gaskets are replaced or resealed. is a good time to replace any leaking seals
try find out what size diff and ratio you have.. its either the X series 5.6" or U series 6" - that refers to the crown wheel outside diameter. the diff ratio is how many times the driveshaft spins compared to the wheels.
if you have a jap import then the diff code should be written on the firewall chassis plate under 'trans/axle'... would have a code like X382 or U312 etc. if you have a 'made in thames' sticker on firewall or a date stamp where the trans/axle is written then its nz new and wont tell you the diff details.
to check ratio. with a locker... with diff in the air and handbrake off, mark a spot on the flange where the driveshaft bolts to diff and the diff itself so you can see how many times it has turned. do the same to a drum and the backing plate. then turn the driveshaft and count how many turns it takes to spin the wheels one rotation.. it should be somewhere between 3.3 to 4.5 turns. you could possibly get more accuracy by turning the wheel twice round and halving the amount of rotations of driveshaft.
if you have open diff then it a bit more tricky. you can do it by holding one wheel, probly easiest to sit it on a block of wood whilst the other wheel in the air. turn the driveshaft and count the turns but do two rotations of the wheel to get the ratio number.
if you happen to take diff head out then the ratio is written on the crownwheel. (may need to rub oil off to be able to see it) either in a 4mm dia circle with a number in it or will have a teeth count number like 41/9 which when divided will give ratio (that one would be a 4.55:1). once you know what it is you can try find one the same.
its not that important to find same ratio (well against law for speedo to be out) but is nice to keep speedo accurate if you have kept factory tyre size.
$50 is ok price. pickapart sell diff head for $42 in aucks.
can check wear by how much backlash there is between the teeth. it hard to explain how much is too much tho
em hope that helps? borrow or buy a corolla or starlet workshop manual for instruction on how to replace a diff head in detail.