You have to do the Ability Check.
The rule in the DMG (page 200) that you quoted has the solution (emphasis mine):
If the spell is on your class's spell list but of a higher level than you can normally cast, you must make an ability check using your spellcasting ability to determine whether you cast it successfully. The DC equals 10 + spell's level. On a failed check, the spell disappears from the scroll with no other effect.
Take a look at the rules for multiclassing in PHB (page 164) too (emphasis mine):
If you have more than one spellcasting class, 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.
Here, since you have two different spell lists (which may overlap, in this case):
- Druid's list, you known and can prepare spells up to 5th level
- Cleric's list, you known and can prepare spells up to 1st level
Since you total level is 10 (or 11\$^1\$), you have 5th spell slots available, but you can cast only 1st level spells from the cleric's list. If you try to cast a Cleric spell\$^2\$ of level greater than 1 from a scroll, then the enlighten parts of the rule for casting from a scroll applies: the spell is in your class list, but it has an higher level than the one you can normally cast as a cleric, not as a character of level 10 (or 11).
Consider, for example, a scroll with Daylight: it is a 3rd level spell and it belongs to both cleric and druid lists. You can decide which class use to read this scroll: as a druid, you have no ability check to do, while as a cleric a 3rd level spell is beyond your maximum and then you have to do the ability check.
Another interesting point refers to Casting a Spell at a Higher Level:
When a spellcaster casts a spell using a slot that is of a higher level than the spell, the spell assumes the higher level for that casting.
This does not contradict the above ruling, since the wording higher level than you can normally cast does not apply here: in the OP case, the character can not normally cast (i.e., prepare and cast) 5th level Cleric spells, but only 1st level ones using a 5th level slot. This rule refers to special cases when the effective casting level matters (e.g., 3rd level Counterspell against an empowered 5th level Fireball).
\$^1\$ Depending on your Druid level when you decided to multiclass.
\$^2\$ By as a Cleric spell I mean as a spell belonging to the Cleric's list, as clarified also in the Spells Known and Prepared section here (emphasis mine):
[...] Each spell you know and prepare is associated with one of your classes, [...]