1, what do you mean 'going through the old Apple ID' ?
You can reset an account's password via http://iforgot.apple.com
You can't delete an account, you can only remove any personal info from it and stop using it - all content that was downloaded with it will remain tied to it.
2, you can't permanently delete any item from your purchase history, all you can do is hide them via your computer's iTunes : iTunes Store: Hiding and unhiding purchases
3, delete them from where ? If you mean your support profile then you can log into your account and remove them : https://supportprofile.apple.com/
If you mean the 'manage devices' section of your account then you can remove them by logging into the account via your computer's iTunes : iTunes Store: Associating a device or computer to your Apple ID
1: sorry I meant that some apps/music are still being downloaded via the old Apple ID, I've no idea as I've not used that Apple ID for years, the only Apple product I have now is iPhone 5s which I got last week, I'm logged in with the new Apple ID (or I should say the one I'm using) I've forgotten the old Apple ID password so I can't log into it as I don't have that email no more as it got hacked
2: ok thank you
3: remove them from everywhere that they may be stored as I no longer have an iPad, iPod or iPhone 4s
i appreciate your help, thank you
1, they are items that you are trying to download with your new account but are being linked to the old account when downloaded ? That shouldn't happen, only the account that is currently logged in should be able to download items, and any items that are downloaded should show as linked to that account - and you are getting the account id from 'get info' (control-I) on the items in your library ?
3, the two things that I mentioned (and their links) should be all that you need to do i.e. remove them from your support profile, and (though probably not strictly necessary as I'm not aware of anything that it affects) the 'manage devices' section.
Depending upon what apps that you have on your 5S, check that you haven't got any auto-renewing subscriptions that you were using on your old devices and no longer want (and if necessary stop them renewing) : iTunes Store: Purchasing and managing auto-renewing subscriptions
1: I know that's why I can't understand, I don't know what you mean by "and you are getting the account ID from 'get info' (control-l) on the items in your library?"
when I got my new 5s last week I set up in shop and transferred all my games/music etc and it was showing up I had downloaded 'bubble witch saga 2' from the old Apple ID which is impossible in my eyes as I haven't used the old Apple ID in over 3yrs and I only downloaded that game about 2 month ago
3: thank you
1, for the items that you have downloaded into your computer's iTunes, you can select/highlight one of them and do 'get-info' (press control-I if using a PC, command-I if using a Mac) and you should get a popup with the item's details on it - on the Summary tab on that popup there should be 'apple id' and 'purchase date' (which appears to be date last downloaded) fields