Will there be any issues installing the software on this Mac?
I take it that you mean Final Cut Studio 1, which includes Final Cut Pro 5?
Yes, there will be issues. The most important being that it will not work on an Intel based Mac Book Pro. That version of the suite was written for the long discontinued Power PC equipped Macs.
If this is a full version of the suite, you can buy an upgrade copy to Studio 1.5 or Studio 2 which are for both PPC and Intel or the last version, Studio 2009 (sometimes referred to as Studio 3) which is Intel only. That of course depends if you can actually find a copy as they have all been discontinued.