Can i install 32 bit windows 7 with i5 processor, heard it will not support 32 b

you can install 32 bit windows 7 in a core i5 system, but you will miss the advantages of a 64 bit system. for example your 32 bit os will not be able to utilize more ram (4+ gb). a lot fo newer softwares are 64 bit, you won't be able to run them.
Today's 32-bit Intel and AMD chips can address up to 4GB of memory (an Apple G4 unit can address 2GB). In Windows-based machines, that 4GB is split between the operating system and the applications. That means the most memory any given application can access is 2GB.
xp will run on a core i5 machine, but it will limit it's potential a lot.
you will benefit more from a 64 bit windows 7 home premium or professional.
if you must use xp, create a 2nd boot partition or use xp mode or use a virtualization software.
edit: the quote is from an old pcworld article.