OK so i have found a SOLUTION to this problem that worked for me. I hope this works for others. I got this from the T Mobile page. I have a Galaxy S5 SM G900T, and whenever someone texted me a picture, I would get a download button, and when I pressed it, it would say downloading for along time and I would never get the picture. If you follow the steps below to add an new Access Point Name, you can leave the old one and try this new one, and if this doesn't solve your problem, just click the old APN to go back to what you were using before.
I have a Verizon Galaxy S5 with a t-mobile sim in there. When i first put in the settings that everyone was giving me, Calls, Text and Internet worked but i could not send/receive MMS/Picture messages. Here are some settings i found that worked: (I am talking about adding a new Access point name)
Name: T-Mobile US LTE
APN: fast.t-mobile.com
Proxy: Not Set (leave blank)
Port: Not set (leave blank)
Username: Not Set (leave blank)
Password: Not set (leave blank)
Server: Not set (leave blank)
MMSC : (I cannot type a link, but this web addy isn't a link, it has to be put in the phone, so type the following starting with: H T T P : / /) mms.msg.eng.t-mobile.com/mms/wapenc
Multimedia message Proxy: Not set (leave blank)
Multimedia message Port : Not set (leave blank)
MCC: 310
MNC: 260
Authentication type : None
***NOW THIS HERE IS THE IMPORTANT PART I HAVE FOUND THAT WORKS. ADD IT EXACTLY LIKE BELOW, NO SPACES****
APN type: default,mms,supl,hipri,admin,mobile
APN Protocol : ipv4/IPv6
APN roaming protocol : IPv4
Bearer: Unspecified
Mobile virtual network operator type: None
press the menu button and click save. Try to send/receive an MMS/Picture Message