How do I filter addresses based on a list of zip codes?

I'm planning to mail some postcards to potential business contacts.

I've got a spreadsheet of 2,500+ addresses with columns including Name, Street Address, City, State, and zip code, etc. that cover the entire state of Colorado. But I only want to send the postcards to people near me and I have a list of around 150 zip codes that I'd like to narrow the list to.

I've tried a number of things and haven't been able to get it to work. Ideally, I could output the filtered list of names and addresses to a new spreadsheet tab.

The name, address and other info are in columns B through W. The list of target zip codes is in column AM.

Any advice on how to get this done? I'm not technical and very frustrated. I can't get the Advanced Filter to do the job. The X & VLOOKUP functions have eluded me.

If you could include an exact formula that only needs a little tweaking, that would be ideal. :-) Thank you!
sample mailing list and zips.xlsx