The 'vaiṣṇave guru pañcakaṃ' might be a reference to the five disciples of Viṣṇu whom he taught the 'Pāñcarātra-doctrine' over a period of five nights.
This reference is found in the Vihagendra (विहगेन्द्र) or Vihagendrasaṃhitā, which is accorded a Sāttvika category (Yes! even Pāñcarātra have tri-guṇa classification), as I discuss in this answer.
Vihagendra-Pāñcarātra-Saṃhitā:-
Chapter I: Verse 30.(b) to 34.(a)
आदौ कृतेयुगे प्राप्ते केशवेन प्रसादिता ॥ ३०.२ ॥ अनन्तो गरुडश्चैव
विष्वक्सेनःकपालभृत् । ब्रह्मा इत्येव पञ्चैते शृण्वन्ति पृथगीरितम् ॥ ३१
॥ अनन्तः प्रथमे रात्रौ गरुडश्च द्वितीयके । तृतीयरात्रे सेनेशश्चतुर्थे
वेधसा श्रुतम् ॥ ३२ ॥ रुद्रःपञ्चमरात्रे च श्रुत्वा शास्त्रं पृथक् पृथक्
। ज्ञानयोगक्रियाचार्याग्रन्थं शतसहस्रकम् ॥ ३३ ॥ पञ्चलक्षप्रमाणं
स्यात्पाञ्चरात्रमिति स्मृतम् ॥ ३४.१ ॥
At the beginning of Kṛta-Yuga (Satyuga), by grace of god Keśava
(Viṣṇu), the five disciples, viz. Ananta (Śeṣa-Nāga), Garuḍa,
Viṣvaksena, Brahmā, and Śiva (kapālabhṛt) - heard the various
treatises (śastras) of Pāñcarātra doctrine. On the first night -
Ananta, second - Garuḍa, third - Viṣvaksena, fourth - Brahmā, and
fifth - Śiva, respectively, were bestowed with the treatises
constituting lakhs of verses each - on 'Supreme-knowledge', 'Yoga',
'Rituals' and 'Conduct'. Since the complete set of instruction were
given over a period of five nights, therefore, these treatises are
known as Pāñcarātra.
Accordingly, the above-mentioned 'five disciples'must be revered as gurus or preceptors of the Vaiṣṇava-doctrine lineages.
Therefore, the five Vaiṣṇava Gurus are -
Night 1. Ananta (Śeṣa)
Night 2. Garuḍa
Night 3. Viṣvaksena
Night 4.
Brahmā
Night 5. Rudra (Śiva).