Finding Affordable Tools to Enrich LinkedIn Contacts with Emails

Hi all, my client wants to find the email addresses of 5,120 people he knows on LinkedIn. We have their first and last names, company names, and LinkedIn URLs, but no domains/website links. I know I can use Clay to enrich them with emails, but I'd like to save my Clay credits. Are there cheaper tools I can use for this? I also know ContactOut can help, but the export limit is too low.