You can't just guess what equipment you need for a 5K lab like you can on a $200 one. With a $200 bench, it easy as was a very limited budget, but also for a beginner getting started into basic electronics. 5k is a whole another league and usually goes way over for decent preforming equipment. So really depends on what you are trying to accomplish with the lab and area of research. Just for Spectrum Analyzer, could kill your budget. Then you may need a LCR meter's, a decent scope but would need to know bandwidth needed and they can cost 10k plus even to get one with low now noise, high BW, hardware FFT and ETC. Separate logic analyzer. Then you may need a electronic load and good programmable power supply, or a variable isolation transformer, or a good precision signal generator with low distortion, or a good frequency counter with 10, or 12 digits of frequency resolution and a good one cost money. You may need a good bench meter for data logging could be 6 1/2, or better which will cost money, or a 5 1/2 meter, or don't need a bench meter at all and go with a handheld, you will most likely need a very good solder station especially if your dealing with SMD components as need good thermal recovery and ETC. Did not even get into the specialty tools yet, or calibration, or reference equipment that maybe needed.
5k is could be enough to have decent lab, but solely depend on what you need, if your willing to wait and buy used some equipment. We need to know is what your looking to design, or research and B/W and resolution needed, this affects price widely. Then can better determine and give you a good recommendation on what T&M equipment would be best suited for your needs. You can't just guess, as you find most of the stuff you would have bought will end up being dust collectors, or a paper weight and then realize you needed something else and now don't have it, as you blew your budget. You best bet is buy what you need now and then slowly buy equipment as you see needed.
I would start by buying the basics like good reasonable quality solder station, doesn't have to be the $500 plus one, but can get for example a Hakko FX888D-23BY that will cost around $100 buck and will do the job in most cases, a decent hot air rework station is also a good investment, as will be needed down the road. Then would look into a decent tripe output programmable power supply like a Rigol DP832, which will cost around $400 bucks, others will cost around the same as well for a decent one, unless you get lucky and score one on eBay cheap. Reason why I won't complete dismiss used gear completely, I won't buy anything to old, as can be a hassle with repairing it. You will need a multimeter like a fluke 87v, or 289, or a Brymen BM869 , so expect to spend another $250 to $400 on one meter alone and you will need two. So will be around $500 to $800 on decent meters. A decent bench meter will cost you around $600, you may get lucky if you willing to wait and score a good working one for $300, or less, that for one. I could tell you a few good scopes and signal generators and ETC, but that where it really based on your needs at that point.
I also hoping you have a suitable bench to work on already, as that a whole another cost and can easily set you back over 1k alone, unless you built one then can shave some cost off.