I am aware that, to use a Spell Scroll, you must have the related spell on (at least one of) your spell list(s). Then, if you have the spell slot to cast it, you succeed automatically; else, you must make an ability check in order to cast it (failure resulting in the scroll being wasted).
Consider this example : A Cleric 5 / Wizard 4 finds a Raise Dead Spell Scroll. The spell is on the Cleric List, but is a fifth level spell. Considering that the cleric-wizard has fifth level slots, but can only pick up to third level cleric spells, would he have to make the ability check to successfully cast the Raise Dead in the Spell Scroll, or would he succeed automatically ?
Best Answer
It does not, you must roll the Ability Check
Multiclass spell slots for a wizard/cleric are determined by the multiclass rules on Page 164 of the PHB (emphasis mine).
This allows you to HAVE higher level spells slots than spells you actually know. But, it also stipulates that you cannot cast a spell of that level from one of your classes but can only upcast lower level spells you actually have.
But why?
Because there is a difference between spell slots and what you can cast due to the Multiclass rules.
As you also stated, the spell scroll rules only state, emphasis mine (DMG, 200)
You have a 5th level spell slot, but you cannot actually cast any 5th level spells. He can neither prepare nor know any 5th level spells. What he can do is upcast a spell he can prepare/know in a 5th level slot. What they can prepare/know is going to be specified by their level in that class.
Crawford confirms
Jeremy Crawford answers a question multiclassed spellcasters and casting from scrolls.
Here is the Q&A:
The case of the scroll and a Cleric 5/Wizard 4
In the case of a scroll, it would work as stated above. You have a 5th level spell slot, but neither of your cases actually enable you to cast a 5th level spell. In order to cast that 5th level spell, you'd need to roll the ability check.
It is clear that you have 5th level spell slots, and I believe it is a reasonable interpreation that you can not cast 5th level spells due to the specific limitation in Multiclassing of "this table might give you spell slots of a level that is higher than the spells you know or can prepare. You can use those slots, but only to cast your lower-level spells"(emphasized in block quote at beginning of answer). A 5th level spell scroll would be off-limits as an automatic cast because of this.
A Cleric 5 can cast 3rd levels spells and a Wizard 4 can cast 2nd level spells.
Combined, you have 4th and 5th level spell slots, but you can only cast up to 3rd level cleric spells or 2nd level Wizard spells. In order to use those higher level slots, you could only upcast the spells you can actually cast.
Spell Scrolls with a cleric spell of up to 3rd level would be auto-cast. Spell scrolls with a Wizard spell of up to 2nd level would be auto-cast. Anything higher than either of those would require an ability check.
You have a 5th level spell slot but cant actually cast 5th level spells as a Wizard or a Cleric. You simply can't cast 5th level spells and having a 5th level spell slot doesn't change that.
Your specific casting class must be able to cast the spell.
Upcasting?
One potential problem comes with the information presented on Page 201 of the PHB:
This seems to imply that 'assumes the higher level for that casting' means that what was once a 2nd level is now a 5th level spell due to the upcast. The problem with this General rule is that it breaks in the face of the Specific Rules of multiclassing, which say you can't cast spells of that level, but you can upcast with that available spell slot. This shows that you don't actually have access to 5th level spells, but can use that slot to upcast and upcast only.
The rule on page 201 is less about you being able to cast higher level spells and more about how to treat an upcast spell when facing a counterspell/dispel magic or something else where the spell level is important. Because of the specific requirements around Multiclassing, it is clear that you can not cast 5th level spells as a Cleric 5/Wizard 4.
Specific beats general?
Usually, we can go with an analysis of Specific beating general. However, in this case we have two specific and competing rules (multiclass spellcasting rules and Scroll Casting Rules.)
The only suggestion as to which is more specific lies in the fact that the spell scroll rules are not assuming a table has engaged the Optional Multiclass rules and was likely written assuming single class which would remove any doubts as to whether or not to roll the Ability Check. Once Multiclass Rules were engaged, they became the specific to override the general casting/Scroll Casting rules.