Safi, KE5Z is the report that can meet up your requirement but it will display data if in ORK2 i.e. Profit Center Customizing, control parameters for actual posting is activated only then in GLPCA and GLPCT database table values will populate but before activating this you need to check all business implications so i believe there's no way around except for going for Z* report however if you know how to make query report then you can easily fetch the data by using database tables as VBRK, VBRP, BKPF, FAGLFLEXA and FAGLFLEXT. Logic would be you'll pick all invoices from VBRK and VBRP database tables along with their billed qty and other desired customer information, in additional field you'll pick accounting document number i.e. BELNR from BKPF whereas AWKEY would be same as VBRK-VBELN. Now after picking this accounting document number you'll pass this field to FAGLFLEXT and can get profit center, cost center and other controlling area related details. Choice would be yours whether you want to do it at your own via query which would be bit complex but not impossible or take help from your abaper to pursue with this.
NOTE: Here i would like to add that we members are like a family here, we're to help and everybody is free to give suggestions. I think it's not decent enough to pass comments like professor and sarcastic kind of stuff because you can't judge the intention of the person by the way they replied you.
I'm sure you'll get be able to sort this out now. Do let me know if you need any further help on this and revert with your findings accoridngly. Thanks.