Pronunciation is always a bit different from what spelling would suggest. One can call that sloppy pronuncation, but actually this happens, to some extent, also in totally well-educated pronuncation as e.g. in broadcasting or in theatre.
Examples for sloppy (but very common) pronuncation:
Guten Abend --> Nahmt! (Very sloppy)
Grüß Gott --> Sgott! (Happens only in the South, as only people in the South say "Grüßgott" instead of "Guten Tag".)
Entschuldigung! --> Schullijung!
Können Sie mal halten? --> Könnse mal haltn?
Not sloppy but standard German pronuncation
Lehrer --> Leera [roughly so; actually we would need to use phonetic notation to show the fine nuances; the a is not a full a, it is actually a Schwa vowel]
gehen --> gehn (it is completely normal to leave out the second e)
Schwimmflügel --> schwümmflügl
Your example
fünfundvierzig --> fünn-nfirtsich / fünn-wunfirtsich / fümm-wn-fyrtsych and so on.
This is not dialect. Dialect would e.g. be
fünfundvierzig --> fajwa-fyttsk (Swabian, slightly South of Ulm)
Note that very few language have a full congruence of spelling and pronuncation. Take English! A total mess, actually. Even French is more consistent in its spelling-pronuncation relation than English.
A relatively close relation between spelling and pronuncation is to be found e.g. in Serbian (one of the South-Slavonic language). That's because orthographic rules in this language were designed relatively lately in the 19th century, and purposefully based on how people pronounced things in real life. This was done, of course, at the cost of losing sight of etymology. The capital city of Serbia, Belgrade, meaning "White town", as "bjal" is "white" in Slavonic languages, thus has become "Beograd" in Serbian, where the "o" is foreign to etymology, but people in that region tend to pronounce the "l" quite like what you would actually think is an "o".
Another example for a language with close link between pronuncation and spelling is Turkish (more exactly: the Turkish used in Turkey, as there are other forms of Turkish in neighbouring countries). This is because the spelling rules were created just in the early 1920s, when the country moved from Arabic scripture (as in Ottoman Turkish) to modern Latin scripture including many Umlaut-vowels, especially ü and ö:
Müdürmüsünüz? (Are you the boss?)
You pronounce that exactly like that.