This isn't actually to do with the old lenses per se, but with the design of the viewfinder in modern DSLRs. In short, they're optimized for brightness, and assume automatic focusing. The downside is that they're not very accurate for manual focusing — not really showing differences in depth of field below what you get at f/2.8 or so, if even that. You'll see the same behavior with fast modern lenses.

There are third-party replacement viewfinder screens which are made for manual focusing. One of the most popular brands is KatzEye — I've heard nothing but good things about them (except for the occasional gripe about price, because they're not cheap). They have a model specifically meant for your Nikon D5200, and lots of others as well (including Canon, Pentax, and other brands too). These can be ordered in a variety of configurations, and usually include a split-prism focusing aid to help with manual focus.

Of course, there's an inherent problem that most consumer DSLRs have a viewfinder much smaller than that on even consumer-level SLRs (let alone higher end models). That's an artifact of the sensor size (along with price consciousness) and can't really be helped.

Some other questions and answers on this site provide more information:

• How does one get manual focus right with a fast-aperture lens? (and particularly, this answer)
• Why don't DSLRs come equipped with "classic" focusing screens (split prism, etc)?
• How can I accurately focus manually on an APS-C DSLR?
• If I have a recent, mid-range DSLR, then why, if ever, would I need to buy another / better focusing screen?