I have an oster a5 clipper. The motor is running but the blades do not move .What can be the problem? What part do i need to buy?

All clippers run hot. Motor is enclosed, gearbox and friction all add to the heat.

The blade driving lever is certainly supposed to move, if it isn't then take the cover off and check the cam gear, it's really easy to change it.

make sure the blade is clicked into place fully, secondly check to see if the blade is sitting further away from the clipper than usual, it could also be a stripped gear inside the clipper does the lever move when the blade is engaged?

see if the blade and hinge have moved away from the body of the clipper, the two screws either side of the hinge assembly may need tightening, or the main body may need replacing,
If its just one blade then there must be a problem with that blade.

How old is your clipper, Oster clippers need to be adjusted for more power and speed, also what clipper blade are you using to cut the horse hair and how long is the horse hair, Also the blade may not be sharp, some new blade are sharp maybe defective.

wrong blade,

Are you sure you have Andis A5 or did you mean Oster A5 Clipper, if this clipper is A5 Clipper, You need to check the Lever for wear, The front of the Lever show wear on both side, Like white color and is not squad this Lever is worn. Need to replace. This Lever moves the blade side to side fully. if the Lever is worn the blade will not move fully side to side and the cutter blade the smaller blade will stay in the middle with hardly no travel to side to side and will not cut the hair even if you purchase new blades. Also I would like to mention if the Oster Locking Hinge is worn out and don't have the require tension to hold the blade in place the blade will not cut. How do you test the Oster Hinge on a Oster A5 Clipper,
(1) first close the hinge, in close potion with your finger nail try to open the Hinge, if the hinge slightly open or opens loose the Hinge is worn. if the Hinge is good it will not open or move and your nail may just brake your nail.
Many of my customers run into this type of problem, and the problem can be solve easily by checking these parts first.
One more item I would mention here if replace the A5 Hinge make sure you get the A5 Hinge not the Oster 76 Hinge they are driferrent, The A5 Hinge has on the back two wire's sticking out that fit on the Oster Latch for the A5 Hinge, the Oster 76 Hinge would not have these wire's on the back. I recommend replacing the Latch when you replace the Hinge. I hope this helps any body that have a A5 Oster clipper or A Oster 76 Clipper.
I have over 20 years in the repair business of Sharpening & Clipper repair. Mannys Sharpening 323 263-4697

Oster Hinge

A5 Latch

If the blade mover is going when you turn the clipper on than all you need to do is take the blades apart and clean them well with a Oster spray and then oil them. I would recommend cool lube.

The screws on the side of the housing don't serve any purpose other than keeping the brush and spring in the clipper. You can send your blade in for realignment or call 800-830-3678(factory service) and they will help you with all your issues.

across the blades were they contact each other.  WD40 works fine.