Did you install the CC version without realizing it? You can get the latest non CC version from the Adobe Updates page:
Uninstall what you have, now, in case it’s the wrong thing, then download and install LR 5.6 from the link, above, and if you still have issues, then clear out the SLCache folder like you’ve been reading about.
If none of that works, then start an online chat with Adobe and see what they say regarding your specific serial number. It’s possible it’s been blacklisted/disabled for some reason.
I see, so it’s a student version.
The green checkmark indicates that the digits you’ve entered match a possible valid serial number sequence of digits using algorithms within the program, itself.
The develop module disabled happens after Adobe checks their servers or the information cached locally for your license and determines the license isn’t valid for that particular serial number.
Since it’s a student version maybe Adobe doesn’t think you’re still going to school or maybe the serial number has been used too many times, already, or it’s for a region of the world that you’re not currently registering it from. And I don’t know exactly what the rules are, nowadays, but I’d think you wouldn’t be able to use LR student edition forever, so you may need to re-verify you’re still in school, periodically.
You should also actually try the various things being suggested about installing the LR 5.6 update, clearing the SLCache folder, contact Adobe via chat, rather than just disagreeing it won’t work. This is a user-to-user forum. We can only give you suggestions about what to try troubleshoot the issue. If you’re unwilling to try anything or contact Adobe then there’s not much more to say.
Did you go through the process of verification to Adobe that you qualify for the student/academic version? And are you using the serial number you received following verification?