At the risk of repeating some information, I'm leaving a full message here because I found many of the suggestions above to be vague and confusing. This is a step by step of the call that I just put in to Apple to fix this issue with Samsung S5 Galaxies not getting text messages from iPhones. This process should only be necessary if you no longer have possession of your iPhone; if you do, it seems from messages above you can go into your iPhone's settings and turn off iMessage yourself.
NOTE: According to Victoria, the Apple rep who was familiar with the problem and (supposedly, within the next half hour to 24 hours) fixed the problem, iPhone users who have updated to IOS 7.1.1 --not just 7.1, but the 7.1.1 specifically -- will not have this issue, as 7.1.1 fixed the issue causing this disconnect. However, any iPhone user operating under 7.1 or previous systems will not be able to send an S5 Galaxy user a text without an elaborate and individualized process to remove the former iPhone user's iMessage link. So, here's what I did:
1. Called Apple Support at 800-694-7466 (I could not find the section headings/descriptions mentioned by FoxFifth above on the website listed; the sections did not match anything on the page linked to that supplied url)
2. Followed the prompts, which involved giving my phone number (the one now linked to my Galaxy S5 but formerly to my iPhone 4s) and verbally requesting a representative at the appropriate time after the appropriate prompt. NOTE: disregard the warning about a $19 one-time service charge; it will not apply once you speak to someone.
3. Wait for a rep.
4. When the rep answers, say, "I just upgraded from my iPhone (4, 4s, 5, etc.) to a Samsung Galaxy S5 and can no longer receive texts from other iPhone users. I found online that this is because my iMessage is still turned on and I need you to deactivate my iMessage that automatically sends other iPhone users' messages to that old phone, which I no longer have."
5. The rep, who -- if they are anything like Victoria, who said she's done this "quite a lot today, actually" -- will recognize your issue. The rep will send you a text message to your new device, which contains an alphanumeric code that you must read back to the rep to authenticate it. At that time, the rep will put in your iMessage deactivation request; it should (here's fingers crossed) become active within 24 (some users here say 48, so be patient) hours, at which time the problem should disappear.
I hope this is detailed enough to help everyone else out there. Based on the Apple rep's familiarity with my problem, I'm hopeful the process will work as promised. I will update when I know for sure after a day or two that it is (or isn't) working.