I think it can be easier than the above, you don't absolutely need at T3 boarding pass since you are allowed to access the T3 paid-for third party lounges even if flying elsewhere, and HAL have gone to some effort advertising this facility. So you can just say you are going to Club Aspire. Furthermore I'm almost certain that if you simply turn up at T3 and say you are shopping before returing to T5 then that's fine too, though I haven't tried it myself or seen it happen. You won't be able to use Fast Track security at T3, they have to send bills to different airlines so they do need a valid boarding pass there.

For the return to T5, what you need to do in T3 is when you are ready to return, go to the Lounges area, head for Lounge H (which is AA Admirals Club) then there you will see the purple sign for Flight Connections re-advertised. Just follow it around in the usual way to get to T5. Though 2 hours is indeed sensible, the bus trip actually takes 12 minutes and the service frequency is 6 minutes. MCT T3 to T5 is 90 minutes, and T5 conformance is in broad terms 35 minutes. So putting this together, 90 minutes should be more than adequate.

One recent change, and where personal shoppers is definitely a help, is that they can now get you access to T5 when travelling elsewhere, but you do need to be accompanied for this and you're probably buying something of significant value. It is being used to get to Louis Vuitton, for example.