I have created a repository(of which I am the owner). My repository has about 5 contributors. We are able to review the code submitted by the contributors when they submit their pull request.
What I need to know is there a way other than me opening another account and becoming a contributor myself to get the changes I commit to the repository be reviewed by other contributors first before they are added to the repo.
Yes. If you always work in a different branch, then you can submit a pull request for merging that branch into master.
If you want all branches, and not just master, to be code reviewed, then you will need to work in a different repository. The best way to do this is usually not to open a new account that you make a contributor, but to make an organization for the main repository, transfer ownership to that, and make your main account a contributor. This is probably better for larger projects but may be overkill for smaller projects.
Either way, you can set the repository to protect the master branch and require code review for all commits by everybody (though since you’ll retain control over the repository, you can always bypass this by un-setting that first).