Will a Dell Precision T5500 handle 4K ?

The simple answer is NO. Both of your systems are now outdated and/or obsolete. In fact, the ENTIRE Quadro FX series of GPUs are now too old to be supported at all in the MPE GPU acceleration in CC 2015.3 or later; thus, you would be permanently locked to the MPE software-only mode with that GPU in newer versions of Premiere Pro CC (2015.2 was the last version that supported the legacy Tesla-architecture GPUs for MPE GPU acceleration). What's more, that first-generation Nehalem quad-core CPU is clocked way too low to do much if anything (as far as video editing is concerned); in fact, that quad-core needs to be clocked at 4.0 GHz or higher just to comfortably handle even 1080p.

With all that said, you could still do 4K editing. Just be prepared to wait an excruciatingly long time (say, 10 hours or more for each hour of video content) for the rendering to be completed.