Modified by logo maker. Changes include: compressed width, lower case centered at mid height of capitals, swash terminal on final _g_.

Looks like numbers produced by a sequential numbering machine.
In the style of Clarendon, available from various foundries.
No free version of Clarendon with the matching numbers.

Presumably from a Diploma. These generally use custom wordmarks, often in blackletter styles similar to this.
Smaller institutions can use diplomas from suppliers that have private fonts in this general style.
As for substitutes -- none are an exact match to _University of Califoria_ -- look to a lighter weight of Old English such as Wedding Headline, Wedding Text or Linotext.

User edited to fit logo format

user modified _h_ to add bar matching cross stroke on _t_

Foro Sans Light is another possible substitute for the bottom two lines. It is spot on for _6_and _S_. Top serifs different on _1_ & _7_.

Looks like a business card with engraver's lettering.
Presumably after 1963, when five-digit ZIP Codes were introduced in the U.S.
AFAIK no digital match.
Closest font to the bottom two lines is perhaps Haboro Sans Ext Regular. It is spot on for the top and middle of _5_. Top serifs different on _1_ & _7_.

According to _The Economist_:
“Our logo
The corporate logotype of The Economist has evolved from the gothic lettering used on the cover of the first issue, published in 1843, to the box device designed in 1959 by Reynolds Stone, a British engraver and typographer. It now incorporates a font from The Economist Typefamily, a typeface created specifically for our use.”

https://www.economist.com/help/about-us

Width expanded by logo maker.

AFAIK the Olivetti Lettera typewriter typeface has not been made into a digital font.
Italian Typewriter is based on another Olivetti or very similar typeface.
The letters and numbers are an approximate match to your image. The most noticeable exceptions are 1WwMm.
The font is not offered in a fuzzy version. You would have to produce an image using Italian Typewriter and process the image with a photoshop or Illustrator type program to produce the fuzzy letters you want.

Waltari, a revival of Walthari, designed by Heinz König and originally published by Klingspor foundry in 1899

Old English, available from several foundries. Based on Caslon Black, a Blackletter type cast by the William Caslon foundry in England around 1760.
Customized by using a period to replace the dot on the _i_.

aka Samoa: ATF catalog 1897 p235
Harquil [suggested by jerseygirl] was the name used by John Haddon & Co. a British foundry.

Custom label.
No match to a retail font.
Bessemer Bold is a chamfered font, i.e. clipped angular corners, with a similar weight, width and mid height diagonal for _S_. For similar _A_ imagine a vertical flip of _U_ and add a crossbar.
N.B. the IPA label dos NOT appear to be derived from Bessemer Bold.
Hudson NY is another similar font.

With custom leg on _k_